a local central limit theorem on the laguerre hypergroup abstract we consider here the laguerre hypergroup k where k 0 r and a convolution product on k coming from the product formula satisfied by the laguerre functions l m m n 0 we set on this hypergroup a local central limit theorem which consists to give a weakly estimate of the asymptotic behavior of the convolution powers k k times being a given probability measure satisfying some regularity conditions on this hypergroup it is also given a central local limit theorem for some particular radial probability measures on the 2 n 1 dimensional heisenberg group h n

positive solutions of periodic boundary value problems for nonlinear first order impulsive differential equations abstract motivated by liu y liu further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations j math anal appl 327 2007 435 452 li et al x li x lin d jiang x zhang existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects nonlinear anal 62 2005 683 701 and liu and ge y liu w ge stability theorems and existence results for periodic solutions of nonlinear impulsive delay differential equations with variable coefficients nonlinear anal 57 2004 363 399 this paper is concerned with the periodic boundary value problem pbvp for short for the nonlinear impulsive differential equation x t a t x t f t x t a e t 0 t t 1 t p x t k x t k x t k i k x t k k 1 p x t x 0 we obtain new sufficient conditions for the existence of at least one two or three positive solutions of the above pbvp respectively examples are presented to illustrate the main results

eigenvalue problems for nonlinear differential equations on a measure chain abstract values of are determined for which there exist positive solutions of the second order differential equation on a measure chain u t a t f u t 0 t 0 1 satisfying either the conjugate boundary conditions u 0 u 1 0 or the right focal boundary conditions u 0 u 1 0 where a and f are positive valued and both lim x 0 f x x and lim x f x x exist

on the strong discontinuity approach in finite deformation settings taking the strong discontinuity approach as a framework for modelling displacement discontinuities and strain localization phenomena this work extends previous results in infinitesimal strain settings to finite deformation scenarios by means of the strong discontinuity analysis and taking isotropic damage models as target continuum stress strain constitutive equation projected discrete tractions displacement jumps constitutive models are derived together with the strong discontinuity conditions that restrict the stress states at the discontinuous regime a variable bandwidth model to automatically induce those strong discontinuity conditions and a discontinuous bifurcation procedure to determine the initiation and propagation of the discontinuity are briefly sketched the large strain counterpart of a non symmetric finite element with embedded discontinuities frequently considered in the strong discontinuity approach for infinitesimal strains is then presented finally some numerical experiments display the theoretical issues and emphasize the role of the large strain kinematics in the obtained results copyright 2003 john wiley sons ltd

inversion of the radon transform on the laguerre hypergroup by using generalized wavelets abstract we consider the radon transform r 0 on the laguerre hypergroup k 0 r we characterize a space of infinitely differentiable and rapidly decreasing functions together with their derivatives such that r is a bijection from this space onto itself we establish an inversion formula and a plancherel theorem for the operator r finally by using the continuous wavelet transform on the laguerre hypergroup k we deduce another expression for the inverse r 1 of the operator r

on boundary value problems of second order perturbed dynamic inclusions on time scales abstract in this paper an existence criterion is established for a class of second order perturbed dynamic inclusions on time scales with boundary conditions the main approach is a fixed point theorem for multi valued maps due to dhage

eigenvalue problem for p laplacian three point boundary value problems on time scales abstract let t be a time scale such that 0 t t 0 and 0 t we consider the following p laplacian three point boundary problem on time scales p u t h t f u t 0 t 0 t u 0 u 0 u u t 0 where p 1 0 h c ld 0 t 0 and f c 0 0 some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established in doing so the usual restriction that f 0 lim u 0 f u p u and f lim u f u p u exist is removed an example is also given to illustrate the main results

a cartesian parametrization for the numerical analysis of material instability summary we examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor we then propose a cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition this parametrization is then used to construct a tensor akin to the acoustic tensor it is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability the performance of the cartesian parametrization is compared against the other parametrizations with the results of these comparisons showing that in general the cartesian parametrization is more robust and more numerically efficient than the others copyright 2016 john wiley sons ltd

multiple positive solutions for p laplacian m point boundary value problems on time scales let t be a time scale such that 0 email protected t a i 0 for i 1 m 2 let x i satisfy 0 x 1 x 2 x m 2 r t and i 1 m 2a i 1 we consider the following p laplacian m point boundary value problem on time scales f p u d t a t f t u t 0 email protected 0 t u 0 0 f p u d t email protected i 1m 2a email protected p u d x i where email protected c l d 0 t 0 and email protected c l d 0 t x 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and leggett williams fixed point theorems respectively in particular our criteria extend and improve some known results

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

existence of positive solutions for nonlinear three point problems on time scales in this paper by using fixed point theorems in cones we study the existence of at least one two and three positive solutions of a nonlinear second order three point boundary value problem for dynamic equations on time scales as an application we also give some examples to demonstrate our results

multiple positive solutions for nonlinear singular m point boundary value problem abstract in this paper we study the existence of multiple positive solutions for the following nonlinear m point boundary value problem bvp u a t f u t 0 0 t 1 u 0 i 1 m 2 a i u i u 1 i 1 k b i u i i k 1 s b i u i i s 1 m 2 b i u i where r r is an increasing homeomorphism and homomorphism and 0 0 1 k s m 2 a i b i 0 with 0 i 1 k b i i k 1 s b i 1 0 i 1 m 2 a i 1 0 1 2 m 2 1 a t c 0 1 0 f c 0 0 some new results are obtained for the existence of at least twin or triple positive solutions of the above problem by applying avery henderson and a new fixed point theorems respectively as an application some examples are included to illustrate the main results in particular our results extend and improve some known results

embedded crack vs smeared crack models a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias this paper is concerned with an analysis of the mesh dependence of results from numerical failure analyses using the strong discontinuity approach sda based on an analytical and numerical comparison with a standard plasticity model pertaining to the classical fracture energy based smeared crack concept using a consistent characteristic length the sda is characterized by incorporating the kinematics of fractured solids locally within the finite element the resulting jumps in the displacement field are captured by their corresponding singularly distributed strains for the analytical and numerical study of the mesh dependence only mode i failure is considered analogies and differences of both finite element formulations are investigated and evaluated

a novel algorithmic framework for the numerical implementation of locally embedded strong discontinuities in this paper a novel algorithmic framework for the numerical modeling of locally embedded strong discontinuities suitable for the analysis of material failure such as cracking in brittle structures or shear bands in soils is proposed based on the enhanced assumed strain eas concept the final failure kinematics of solids approximated by discontinuous displacement fields are incorporated into the finite element formulation in contrast to previous works the discontinuous part of the deformation mapping is condensed out at the material level without employing the standard static condensation technique as a consequence the resulting constitutive equations are formally identical to those of standard plasticity models hence the return mapping algorithm is applied to the numerical implementation only slight modifications of this by now classical algorithm are necessary the proposed framework is applicable to any constitutive equation characterizing the inelastic part of deformation referring to the yield failure function and the evolution equations no special assumption has to be made despite the differences between the presented numerical framework and the original implementation of the strong discontinuity approach sda it is shown that both finite element models are completely equivalent the applicability of the novel algorithmic formulation and its numerical performance are investigated by means of two two dimensional as well as by means of a fully three dimensional numerical analysis of shear band formation

existence of triple positive solutions of two point right focal boundary value problems on time scales we consider the following boundary value problem 1 n 1y d n t 1 p 1f t y s n 1 t email protected a b t y d n a 0 email protected email protected p 1 y d n s b 0 email protected email protected n 1 where n 2 1 p n 1 is fixed and t is a time scale by applying fixed point theorems for operators on a cone existence criteria are developed for triple positive solutions of the boundary value problem we also include examples to illustrate the usefulness of the results obtained

further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations abstract this paper is concerned with the solvability of periodic boundary value problems for nonlinear impulsive functional differential equations x t a t x t f t x t x 1 t x n t t j t 1 t p x t k x t k i k x t k k 1 2 p x 0 x t we obtain sufficient conditions for the existence of at least one solution of problem at resonance and nonresonance cases respectively examples are presented to illustrate the main results

positive solutions for a nonlinear functional dynamic equation on a time scale abstract in this paper we obtain sufficient conditions for the existence of positive solutions to a nonlocal eigenvalue problem for a class of nonlinear functional dynamic equations on a time scale we employ a cone theoretic fixed point theorem to establish our results

multiple positive solutions for nonlinear dynamical systems on a measure chain in this paper we consider the following dynamical system on a measure chain u 1 t f1 t u1 t u2 t 0 t a b u 2 t f2 t u1 t u2 t 0 t a b with the sturm liouville boundary value conditions ui a u i a 0 ui b ui b 0 for i 1 2 some results are obtained for the existence of three positive solutions of the above problem by using leggett williams fixed point theorem

twin solutions of boundary value problems for ordinary differential equations and finite difference equations a new twin fixed point theorem is applied first to obtain the existence of at least two positive solutions for the right focal boundary value problem y f ity 0 0 t 1 y 0 y 1 0 it is applied later to obtain the existence of at least two positive solutions for the analogous discrete right focal boundary value problem 2u k g u k 0 k 0 n u 0 u n 1 0

on the formulation and numerical solution of problems in anisotropic finite plasticity abstract this article discusses an extension of the green naghdi finite plasticity theory to explicitly include anisotropic effects in the stress response yield condition flow rule and hardening rule constitutive models are developed within the context of the extended theory and used in formulating implicit integration algorithms which inherit the characteristics of the classical return mapping scheme of isotropic plasticity representative numerical simulations demonstrate the applicability and predictive capacity of the proposed model in the presence of large plastic deformations

existence theorems for second order discrete boundary value problems abstract this article is concerned with the existence of solutions of boundary value problems for nonlinear second order difference equations of the type p n x n 1 q n x n f n x n where 0 is the ratio of odd positive integers p n and q n are real sequences the authors apply the linking theorem and the mountain pass lemma in the critical point theory and give some new results for the existence of solutions

twin positive solutions of boundary value problems for finite difference equations with p laplacian operator abstract in this paper a new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem p u k a k f u k 0 k 0 n u n 1 0 u 0 b 0 u 0 0 in addition two corollaries and an example are given to illustrate the main results

on the numerical resolution of the discontinuous material bifurcation problem the work focuses on the numerical resolution of the discontinuous material bifurcation problem as a relevant ingredient in computational material failure mechanics the problem consists of finding the conditions for the strain localization onset in terms of the so called bifurcation time localization directions and localization modes a numerical algorithm based on the iterative resolution of a coupled eigenvalue problem in terms of the localization tensor is proposed for such purpose the algorithm is shown to be always convergent to the exact solution for the symmetric case major and minor symmetries of the tangent constitutive operator in the unsymmetric case only minor symmetries the solution is no longer exact although it is shown that using the symmetric part of the localization tensor in the proposed algorithms provides enough accurate solutions for most of cases numerical examples illustrate the benefits of the proposed methodology in terms of accuracy and savings in the computational cost associated with the problem copyright 2010 john wiley sons ltd

multiple positive solutions of quasi linear boundary value problems for finite difference equations abstract in this paper we consider a discrete second order quasi linear boundary value problem which nonlinear term f is involved with the first order difference by using a generalization of the leggett williams fixed point theorem due to avery and peterson we provide sufficient conditions for the existence of at least three positive solutions

numerical analyses of discontinuous material bifurcation strong and weak discontinuities abstract in this paper an algorithmic formulation for numerical analyses of material bifurcation is presented conditions for the onset of both weak discontinuities discontinuous strain rates and strong discontinuities discontinuous velocity fields are summarized based on a recently proposed plasticity model formulated within the logarithmic strain space the condition for the formation of strong discontinuities is extended to anisotropic finite strain plasticity theory the resulting equations associated with the mode of bifurcation are solved numerically for that purpose an equivalent optimization problem is considered the algorithmic formulation is based on newton s method using a consistent linearization to enlarge the radius of convergence a line search strategy is applied the applicability of the proposed implementation as well as its performance and numerical robustness is investigated by means of three dimensional numerical bifurcation analyses of a drucker prager type plasticity model

positive solutions for p laplacian functional dynamic equations on time scales abstract in this paper the authors study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 x t 0 by using the twin fixed point theorem sufficient conditions are established for the existence of twin positive solutions

analysis of slip planes in three dimensional solids abstract three dimensional solids in which displacement jumps develop across planes are analysed critical to such analysis is the identification of the correct orientation of the discontinuity plane to do this strain softening continuum relationships are examined for the limit case of a strong displacement discontinuity which then yields a localisation condition for the introduction of a displacement jump a numerical procedure is proposed to correctly orientate the discontinuity plane in space for the von mises and drucker prager yield criteria traction displacement relationships are developed and implemented by embedding the slip planes in conventional solid finite elements this makes the analysis ideal for large three dimensional calculations the performance of the developed discrete constitutive models and that of the embedded discontinuity elements in three dimensions are scrutinised with special attention paid to mesh objectivity and volumetric locking

existence results for dynamic sturm liouville boundary value problems via variational methods abstract several conditions ensuring existence of solutions of a dynamic sturm liouville boundary value problem are derived variational methods are utilized in the proofs an example illustrating the main results is given

three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales abstract the five functionals fixed point theorem is applied to investigate the existence of at least three positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales

modeling of failure in composites by x fem and level sets within a multiscale framework abstract composites or multi phase materials are characterized by a distinct heterogeneous microstructure the failure modes of these materials are governed by several micromechanical effects like debonding phenomena and matrix cracks the overall mechanical behavior of composites in the linear as well as the nonlinear regime is not only governed by the material properties of the components and their bonds but also by the material layout in the present contribution the material structure is resolved and modeled on a small scale allowing to deal with these effects for the numerical simulation we apply a combination of the extended finite element method x fem n moes j dolbow t belytschko a finite element method for crack growth without remeshing int j numer methods engrg 46 1999 131 150 and the level set method lsm s osher j sethian fronts propagating with curvature dependent speed algorithms based on hamilton jacobi formulations j comput phys 79 1988 12 49 in the x fem the finite element approximation is enriched by appropriate functions through the concept of partition of unity the geometry of material interfaces and cracks is described by the lsm the combination of both x fem and lsm turns out to be very natural since the enrichment can be described and even constructed in terms of level set functions in order to project the material behavior modeled on a small scale onto the large or structural scale we employ the variational multiscale method vmm t hughes g feijoo l mazzei j b quiney the variational multiscale method a paradigm for computational mechanics comput methods appl mech engrg 166 1998 3 24 this concept is based on an additive split of the displacement field into large and small scale parts for an efficient solution of the discrete problem we postulate that the small scale displacements are locally supported in order to achieve this objective one has to assume appropriate constraint conditions it can be shown that the applied numerical model allows a considerable flexibility concerning the variation of the material design and consequently of the mechanical behavior of a composite

triple positive solutions of boundary value problems for p laplacian dynamic equations on time scales a new triple fixed point theorem is applied to investigate the existence of at least three positive solutions of boundary value problems for p laplacian dynamic equations on time scales

existence of positive solutions to second order time scale systems in this paper the author consider the following dynamic system on a measure chain u i d d t f i t u 1 s t u 2 s t u n s t 0 email protected a b satisfying sturm liouville boundary conditions a iu i a email protected iu i d a 0 c iu i s b email protected iu i d s b 0 i 1 2 n some new results are obtained for the existence of single twin and triple positive solutions of the above system by using nonlinear alternative of leray schauder type krasnosel skii s fixed point theorem in a cone and leggett williams fixed point theorem

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

existence of three positive solutions to a second order boundary value problem on a measure chain growth conditions are imposed on f such that the boundary value problem x t f x t t t1 t2 x t1 x t1 0 and x t2 x t2 0 where t1 t2 from a measure chain t has at least three positive solutions by way of the five functionals fixed point theorem

positive solutions of two point right focal boundary value problems on time scales we consider the following boundary value problem 1 n 1y d n t 1 p 1f t y s n 1 t email protected a b t y d i a 0 email protected email protected p 1 y d i s b 0 email protected email protected n 1 where n 2 1 p n 1 is fixed and t is a time scale criteria for the existence of single double and multiple positive solutions of the boundary value problem are developed upper and lower bounds for these positive solutions are established for two special cases that arise from some physical phenomena we also include several examples to illustrate the usefulness of the results obtained

positive solutions of a nonlinear three point boundary value problem in this paper by using the fixed point index theorems we study the existence of at least one or two positive solutions to the three point boundary value problem y t a t f y t 0 0 t 1 y 0 0 y 1 y where 0 1 0 1 as an application we also give some examples to demonstrate our results

a wiener tauberian and a pompeiu type theorems on the laguerre hypergroup abstract a wiener tauberian theorem is proven on the laguerre hypergroup m m nessibi k trimeche inversion of the radon transform on the laguerre hypergroup by using generalized wavelets j math anal appl 208 1997 337 363 as consequence of this theorem we establish a pompeiu type theorem and we study some of its applications

positive solutions for nonlinear three point boundary value problems on time scales abstract let t be a time scale such that 0 t t consider the following three point boundary value problem on time scales u t a t f t u t 0 t 0 t u 0 u 0 0 u u t where 0 0 0 t 0 t and d t 1 0 by using fixed point theorems in cones some new and general results are obtained for the existence of single and multiple positive solutions of the above problem in particular our criteria generalize and improve some known results

multiple positive solutions for p laplacian functional dynamic equations on time scales abstract the authors improve some well known fixed point theorems and study the boundary value problems for a p laplacian functional dynamic equation on a time scale p x t a t f x t x t 0 t 0 t x 0 t t t r 0 x 0 b 0 x 0 0 x t 0 by using the fixed point theorems sufficient conditions are established for the existence of multiple positive solutions

capturing strain localization in dense sands with random density summary this paper presents a three invariant constitutive framework suitable for the numerical analyses of localization instabilities in granular materials exhibiting unstructured random density a recently proposed elastoplastic model for sands based on critical state plasticity is enhanced with the third stress invariant to capture the difference in the compressive and extensional yield strengths commonly observed in geomaterials undergoing plastic deformation the new three invariant constitutive model similar to its two invariant predecessor is capable of accounting for meso scale inhomogeneities as well as material and geometric nonlinearities details regarding the numerical implementation of the model into a fully nonlinear finite element framework are presented and a closed form expression for the consistent tangent operator whose spectral form is used in the strain localization analyses is derived an algorithm based on the spectral form of the so called acoustic tensor is proposed to search for the necessary conditions for deformation bands to develop the aforementioned framework is utilized in a series of boundary value problems on dense sand specimens whose density fields are modelled as exponentially distributed unstructured random fields to account for the effect of inhomogeneities at the meso scale and the intrinsic uncertainty associated with them copyright 2006 john wiley sons ltd

existence of solutions for a first order p laplacian bvp on time scales we introduce a first order delta dynamic equation on time scales involving the one dimensional p laplacian and prove the existence of at least one positive solution an example applying our result is also given

a general framework for the numerical solution of problems in finite elasto plasticity this article discusses a general framework for the analysis of initial boundary value problems of rate independent finite elasto plasticity based on the theory of green and naghdi a constitutive model is developed within the context of the above theory employing generalized measures of lagrangian strain and work conjugate measures of stress computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential algebraic equations of plastic flow representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations

existence of positive solutions of nonlinear m point bvp for an increasing homeomorphism and positive homomorphism on time scales in this paper we will consider the following multipoint boundary value problem for the following second order dynamic equations on time scales f u d a t f t u t 0 t 0 t u 0 i 1m 2a iu x i f u d t i 1m 2b i f u d x i where f r r is an increasing homeomorphism and positive homomorphism and f 0 0 by using fixed point theorems we obtain an existence theorem of positive solutions for the above boundary value problem which includes and improve some related results in the relevant literature as an application an example to demonstrate our results is given

extremal solutions for the difference φ laplacian problem with nonlinear functional boundary conditions abstract in this paper we study the existence and approximation of the extremal solutions for the laplacian problem lying between a pair of a lower solution and an upper solution such that we consider general boundary functional conditions that include classical ones as separated or periodic

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

double positive solutions of n p boundary value problems for higher order difference equations abstract we shall provide existence criteria for double positive solutions of the n p boundary value problem n y f k y y n 2 y g k y y n 1 y n 1 k n i y 0 0 0 i n 2 p y n n p 0 where n 2 and 0 p n 1 is fixed upper and lower bounds for the two positive solutions are also established for a particular boundary value problem when n 2 several examples are included to dwell upon the importance of the results obtained

on sturm liouville boundary value problems for second order nonlinear functional finite difference equations motivated by the interesting paper i karaca discrete third order three point boundary value problem j comput appl math 205 2007 458 468 this paper is concerned with a class of boundary value problems for second order functional difference equations sufficient conditions for the existence of at least one solution of a sturm liouville boundary value problem for second order nonlinear functional difference equations are established we allow f to be at most linear superlinear or sublinear in obtained results

periodic solutions of second order discrete convex systems involving the p laplacian some existence theorems are obtained for periodic solutions of second order discrete convex systems involving the p laplacian by using the dual least action principle

triple positive pseudo symmetric solutions of three point bvps for p laplacian dynamic equations on time scales abstract let t be a time scale such that 0 t t we consider the three point boundary value problem for p laplacian dynamic equations on time scales t of the form p u t h t f t u t 0 for t 0 t t with boundary conditions u 0 0 u u t where t is symmetric in t t and p u u p 2 u with p 1 by using a pseudo symmetric technique and the five functionals fixed point theorem we prove that the boundary value problem has at least three positive pseudo symmetric solutions under some assumptions as an application an example is given to illustrate the result

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

solutions for higher order dynamic equations on time scales let t be a time scale we study the existence of positive solutions for the nonlinear four point singular boundary value problem with higher order p laplacian dynamic equations on time scales by using the fixed point index theory the existence of positive solution and many positive solutions for nonlinear four point singular boundary value problem with p laplacian operator are obtained

twin solutions of boundary value problems for differential equations on measure chains a new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the right focal boundary value problem on a measure chain t y t f y t 0 t 0 1 t y 0 y 1 0

finite element simulation of strain localization with large deformation capturing strong discontinuity using a petrov galerkin multiscale formulation the finite element model for strain localization analysis developed in a previous work is generalized to the finite deformation regime strain enhancements via jumps in the displacement field are captured and condensed on the material level leading to a formulation that does not require static condensation to be performed on the element level a general evolution condition is first formulated laying out conditions for the continued activation of a strong discontinuity then a multiscale finite element model is formulated to describe the post bifurcation behavior highlighting the key roles played by the continuous and conforming deformation maps on the characterization of the finite deformation kinematics of a localized element traced by a strong discontinuity the resulting finite element equation exhibits the features of a petrov galerkin formulation in which the gradient of the weighting function is evaluated over the continuous part of the deformation map whereas the gradient of the trial function is evaluated over the conforming part of the same map in the limit of infinitesimal deformations the formulation reduces to the standard galerkin approximation described in a previous work numerical examples are presented demonstrating absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions 2002 elsevier science b v all rights reserved

triple positive solutions for p laplacian m point boundary value problem on time scales in this paper we discuss the following p laplacian m point boundary value problem on time scales t f p u d t h t f t u t u d t 0 email protected 0 t t u 0 0 f p u d t email protected i 1m 2a email protected p u d x i where f p u u p 2u for p 1 some new existence criteria for at least three positive solutions are established by using a generalization of the leggett williams fixed point theorem due to bai and ge an example is also given to demonstrate the main result

positive solutions of nonlinear m point bvp for an increasing homeomorphism and homomorphism with sign changing nonlinearity on time scales in this paper several existence theorems of positive solutions are established for nonlinear m point boundary value problem for the following dynamic equations on time scales f u d a t f t u t 0 t 0 t f u d 0 i 1m 2a i f u d x i u t i 1m 2b iu x i where f r r is an increasing homeomorphism and homomorphism and f 0 0 the nonlinear term f may change sign as an application an example to demonstrate our results is given

existence theory for positive solutions to one dimensional p laplacian boundary value problems on time scales abstract in this paper we consider the one dimensional p laplacian boundary value problem on time scales p u t h t f u t 0 t a b u a b 0 u a 0 u b 0 where p u is p laplacian operator i e p u u p 2 u p 1 some new results are obtained for the existence of at least single twin or triple positive solutions of the above problem by using krasnosel skii s fixed point theorem new fixed point theorem due to avery and henderson and leggett williams fixed point theorem this is probably the first time the existence of positive solutions of one dimensional p laplacian boundary value problems on time scales has been studied

a self consistent eulerian rate type model for finite deformation elastoplasticity with isotropic damage abstract continuum models for coupled behaviour of elastoplasticity and isotropic damage at finite deformation are usually formulated by first postulating the additive decomposition of the stretching tensor d into the elastic and the plastic part and then relating each part to an objective rate of the effective stress etc it is pointed out that according to the existing models with several widely used objective stress rates none of the rate equations intended for characterizing the damaged elastic response is exactly integrable to really deliver a damaged elastic relation between the effective stress and an elastic strain measure the existing models are thus self inconsistent in the sense of formulating the damaged elastic response by consistently combining additive and multiplicative decomposition of the stretching d and the deformation gradient f and adopting the logarithmic stress rate in this article we propose a general eulerian rate type model for finite deformation elastoplasticity coupled with isotropic damage the new model is shown to be self consistent in the sense that the incorporated rate equation for the damaged elastic response is exactly integrable to yield a damaged elastic relation between the effective kirchhoff stress and the elastic logarithmic strain the rate form of the new model in a rotating frame in which the foregoing logarithmic rate is defined is derived and from it an integral form is obtained the former is found to have the same structure as the counterpart of the small deformation theory and may be appropriate for numerical integration the latter indicates in a clear and direct manner the effect of finite rotation and deformation history on the current stress and the hardening and damage behaviours further it is pointed out that in the foregoing self consistency sense of formulating the damaged elastic response the suggested model is unique among all objective eulerian rate type models of its kind with infinitely many objective stress rates to be chosen in particular it is indicated that within the context of the proposed theory a natural combination of the two widely used decompositions concerning d and f can consistently and uniquely determine the elastic and the plastic parts in the two decompositions as well as all their related kinematical quantities without recourse to any ad hoc assumption concerning a special form of the elastic part f e in the decomposition f f e f p or a related relaxed intermediate configuration as an application the proposed general model is applied to derive a self consistent eulerian rate type model for void growth and nucleation in metals experiencing finite elastic plastic deformation by incorporating a modified gurson s yield function and an associated flow rule etc two issues involved in previous relevant literature are detected and raised for consideration as a test problem the finite simple shear response of the just mentioned model is studied by means of numerical integration

triple solutions for second order three point boundary value problems abstract we establish the existence of at least three positive solutions to the second order three point boundary value problem u f t u 0 u 0 0 u u 1 where 0 lt f 0 1 0 0 is continuous we accomplish this by making growth assumptions on f which can apply to many more cases than the sublinear and superlinear ones discussed in recent works

a finite element model for strain localization analysis of strongly discontinuous fields based on standard galerkin approximation abstract this paper presents a finite element model for strain localization analysis of elastoplastic solids subjected to discontinuous displacement fields based on standard galerkin approximation strain enhancements via jumps in the displacement field are captured and condensed on the material level leading to a formulation that does not require static condensation to be performed on the element level the mathematical formulation revolves around the dual response of a macroscopic point cut by a shear band which requires the satisfaction of the yield condition on the band as the same stress point unloads elastically just outside the band precise conditions for the appearance of slip lines including their initiation and evolution are outlined for a rate independent strain softening drucker prager model and explicit analytical expressions are used to describe the orientation of the slip line in a plane strain setting at post localization the stress point integration algorithm along the band is exact and amenable to consistent linearization numerical examples involving simple shearing of elastoplastic solids with deviatoric plastic flow as well as plane strain compression of dilatant cohesive frictional materials are presented to demonstrate absolute objectivity with respect to mesh refinement and insensitivity to mesh alignment of finite element solutions

double positive solutions for a nonlinear four point boundary value problem with a p laplacian operator in this paper we study the existence of positive solutions for a nonlinear four point boundary value problem with a p laplacian operator by using a three functionals fixed point theorem in a cone the existence of double positive solutions for the nonlinear four point boundary value problem with ap laplacian operator is obtained this is different than previous results

constructive proof for existence of nonlinear two point boundary value problems owing to the importance of differential equations in physics the existence of solutions for differential equations has been paid much attention in this paper the existence of solution are obtained for the nonlinear second order two point boundary value problem in the reproducing kernel space under certain assumptions on right hand side we propose constructive proof for the existence result and a method is presented to obtain the exact solution expressed by the form of series this paper is a extension of previous paper wei jiang minggen cui the exact solution and stability analysis for integral equation of third or first kind with singular kernel appl math comput 202 2 2008 666 674 which extends a method of solving linear problems to present method for solving nonlinear problems

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

3d modelling of strong discontinuities in elastoplastic solids fixed and rotating localization formulations this paper is concerned with the incorporation of displacement discontinuities into a continuum theory of elastoplasticity for the modelling of localization processes such as cracking in brittle materials based on the strong discontinuity approach sda computational mechanics 1993 12 277 296 mesh objective 2d and 3d finite element formulations are developed using linear and quadratic 2d elements as well as 8 noded 3d elements in the formulation of the finite element model proposed in the paper the analogy with standard formulations is emphasized the parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique this approach results in linearized constitutive equations formally identical to continuum models therefore the standard return mapping algorithm is used to solve the non linear equations in analogy to concepts used in continuum smeared crack models a rotating formulation of the sda is proposed in addition to the standard concept of fixed discontinuities it is shown that the rotating localization approach reduces locking effects observed in analyses based on fixed localization directions the applicability of the proposed sda finite element model as well as its numerical performance is investigated by means of a three dimensional ultimate load analysis of a steel anchor embedded in a concrete block subjected to a shear force copyright 2003 john wiley sons ltd

multiple positive solutions for functional dynamic equations on time scales in this paper we study the following functional dynamic equation on time scales f u d t a t f u t u m t 0 email protected 0 t t u t email protected t email protected r 0 t u 0 b 0 u d 0 0 u d t 0 where f r r is an increasing homeomorphism and a positive homomorphism and f 0 0 by using the well known leggett williams fixed point theorem existence criteria for multiple positive solutions are established an example is also given to illustrate the main results

triple positive solutions of m point bvps for p laplacian dynamic equations on time scales abstract this paper is concerned with the existence of positive solutions of p laplacian dynamic equation p u t a 1 t f u t 0 subject to boundary conditions u 0 b 0 i 1 m 2 a i u i 0 u t 0 or u 0 0 u t b 1 i 1 m 2 b i u i 0 where p v v p 2 v with p 1 by using the five functionals fixed point theorem we prove that the boundary value problem has at least three positive solutions as an application an example is given to illustrate the result

multiple positive solutions for nonlinear three point boundary value problems on time scales in this paper we consider the nonlinear second order three point boundary value problem u d t h t f t u t 0 t t 1 t 3 t u d t 3 0 au t 1 bu d t 1 u d t 2 where t is a time scale 0 t 10 and b 0 are given constants by using fixed point theorems in cones some new results are obtained for the existence of at least one two and three positive solutions of the above problem

several sufficient conditions of solvability for a nonlinear higher order three point boundary value problem on time scales abstract in this paper a nonlinear higher order three point boundary value problem on time scales is considered under certain growth conditions on the nonlinearity several sufficient conditions for the existence of nontrivial solution are obtained by using leray schauder nonlinear alternative as an application some examples to demonstrate our results are given

periodic and subharmonic solutions for fourth order nonlinear difference equations abstract by using the critical point theory some new criteria are obtained for the existence and multiplicity of periodic and subharmonic solutions to fourth order nonlinear difference equations the main approach used in our paper is a variational technique and the linking theorem our results generalize and improve the existing ones

existence of three positive pseudo symmetric solutions for a one dimensional p laplacian abstract we apply the five functionals fixed point theorem to verify the existence of at least three positive pseudo symmetric solutions for the three point boundary value problem g u a t f u 0 u 0 0 and u u 1 where g v v p 2 v with p 1 and 0 1

double positive solutions of three point boundary value problems for p laplacian dynamic equations on time scales a new double fixed point theorem is applied to investigate the existence of at least double positive solutions of three point boundary value problems for p laplacian dynamic equations on a time scale

anisotropic additive plasticity in the logarithmic strain space modular kinematic formulation and implementation based on incremental minimization principles for standard materials the paper presents a modular formulation and computational implementation of a class of anisotropic plasticity models at finite strains based on incremental minimization principles the modular kinematic setting consists of a constitutive model in the logarithmic strain space that is framed by a purely geometric pre and postprocessing on the theoretical side the point of departure is an a priori six dimensional approach to finite plasticity based on the notion of a plastic metric in a first step a geometric preprocessor defines a total and a plastic logarithmic strain measure obtained from the current and the plastic metrics respectively in a second step these strains enter in an additive format a constitutive model of anisotropic plasticity that may have a structure identical to the geometrically linear theory the model defines the stresses and consistent tangents work conjugate to the logarithmic strain measure in a third step these objects of the logarithmic space are then mapped back to nominal lagrangian or eulerian objects by a geometric postprocessor this geometric three step approach defines a broad class of anisotropic models of finite plasticity directly related to counterparts of the geometrically linear theory it is specified to a model problem of anisotropic metal plasticity on the computational side we develop an incremental variational formulation of the above outlined constitutive structure where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables it is shown that this minimization problem is exclusively restricted to the logarithmic strain space in a structure identical to the small strain theory the minimization problem determines the internal state of the material for finite increments of time we develop a discrete formulation in terms of just one scalar parameter for the amount of incremental flow the existence of the incremental stress potential provides a natural basis for the definition of the geometric postprocessor based on function evaluations furthermore the global initial boundary value problem of the elastic plastic solid appears in the incremental setting as an energy minimization problem numerical examples show that the results obtained are surprisingly close to those obtained by a reference framework of multiplicative plasticity