positive and compacton type solutions for a quasilinear two point boundary value problem abstract in this paper we investigate a one dimensional p laplacian problem whose nonlinearity comprises both p sublinear and p superlinear terms by studying the multiplicity of solutions to an auxiliary problem we show how convenient choices of the parameters involved yield the existence of at least three classical positive solutions satisfying hopf s boundary condition in addition we provide the existence of two distinct curves of parameters along which our problem admits at least a compacton type solution

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 lagrangian and hamiltonian constraint algorithms for the rarita schwinger field coupled to an external electromagnetic field the complete constraint analysis for the rarita schwinger 3 2 field coupled to an external electromagnetic field is given showing the parallel between the lagrangian and dirac bergman algorithms the analysis confirms the connection between the velo zwanzinger 1969 and johnson sudarshan 1961 pathologies and illustrates that these do not in fact arise because the constraint analysis leading to them is incomplete on the contrary a new tier of constraints occurs for the critical field values reducing the pathology to a field induced change in degrees of freedom

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

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

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

a singular boundary value problem for the one dimensionalp laplacian abstract the singular boundary value problem formula is studied in this paper whereg s s p 2s p 1 the singularity may appear atu 0 and att 0 ort 1 and the functionfmay be discontinuous the authors prove that for anyp 1 and for any positive nonincreasing functionfand nonnegative measurable functionkwith some integrability conditions the above mentioned problem has a unique solution also the properties of the solution are discussed in the paper

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

the fredholm alternative at the first eigenvalue for the one dimensionalp laplacian abstract in this work we study the range of the operatoru u p 2 u 1 u p 2 u u 0 u t 0 p 1 we prove that all functionsh c1 0 t satisfying t0 h t sinp pt t dt 0 lie in the range but that ifp 2 andh 0 the solution set is bounded here sin pt t is a first eigenfunction associated to 1 we also show that in this case the associated energy functionalu 1 p t0 u p 1 p t0 u p t0 huis unbounded from below if 1 2 onw1 p0 0 t 1corresponds precisely to the best constant in thelp poincare inequality moreover we show that unlike the linear casep 2 forp 2 the range contains a nonempty open set inl 0 t

multiple positive solutions for nonlinear periodic problems abstract we consider a nonlinear periodic equation driven by the scalar p laplacian and with a caratheodory asymptotically p 1 linear nonlinearity using variational methods coupled with suitable truncation techniques we show that the problem has at least two positive solutions for the semilinear case p 2 using morse theory we show that the problem has three distinct positive solutions

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

existence of positive solutions for singular boundary value problems involving the one dimensional p laplacian this paper studies the existence of positive solutions for singular dirichlet boundary value problems these results are obtained by using the global continuation theorem fixed point index theory and approximate method

positive solutions for a system of higher order multi point boundary value problems we present some results for positive solutions of a system of higher order nonlinear ordinary differential equations subject to multi point boundary conditions

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

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

existence of the second positive radial solution for a p laplacian problem we investigate the existence nonexistence and multiplicity of positive radial solutions for the p laplacian problem with boundary parameters for proofs we mainly use a combination of a fixed point theorem the method of upper and lower solutions and fixed point index theory in the frame of the ordinary differential equation ode technique

correlational kinetics ii boltzmann collision terms abstract a derivation of generalized boltzmann collision terms in correlational kinetics is given such a kinetic theory allows the treatment of correlations for systems of particles even with long ranged and retarded interactions the derivation of the collision terms is based upon a number of assumptions which have already been used in connection with the boltzmann equation

lidstone polynomials and boundary value problems abstract we define lidstone polynomials provide their explicit representations give their relations with bernoulli polynomials obtain best possible error estimates in lidstone interpolation and establish several best possible sharp inequalities which compare favourably with the known results next we use these results to study even order differential equations together with lidstone boundary conditions

sharp conditions for the existence of sign changing solutions to equations involving the one dimensional p laplacian abstract we consider the boundary value problem involving the one dimensional p laplacian u p 2 u a x f u 0 0 x 1 u 0 u 1 0 where p 1 we establish sharp conditions for the existence of solutions with prescribed numbers of zeros in terms of the ratio f s s p 1 at infinity and zero our argument is based on the shooting method together with the qualitative theory for half linear differential equations

a class of multi parameter eigenvalue problems for perturbed p laplacians this paper is devoted to multi parameter eigenvalue problems for one dimensional perturbed p laplacians modelling travelling waves for a class of nonlinear evolution pde dispersion relations between the eigen parameters the existence of eigenfunctions and positive eigenfunctions variational principles for eigenvalues and constructing solutions in the analytical and implicit forms are the main subject of this paper we use both variational and analytical methods

eigenvalues and the one dimensional p laplacian we consider the boundary value problem p u f t u 0 with p 1 t 0 1 u 0 u 1 0 and with 0 the value of is chosen so that the boundary value problem has a positive solution in addition we derive an explicit interval for such that for any in this interval the existence of a positive solution to the boundary value problem is guaranteed in addition the existence of two positive solutions for in an appropriate interval is also discussed

radial solutions for the p laplacian equation abstract we study the existence of positive solutions of the following nonlinear equation 1 a a p u u in 0 where p 1 0 p x x x p 2 and a satisfies some appropriate conditions our purpose is to give two existence results for the above equation subject to some boundary conditions where the nonlinear term is a nonnegative continuous function in 0 0 satisfying some adequate hypotheses

singular second order boundary value problems many other boundary conditions could be considered however since the analysis is similar we choose to omit the details for example if b denoted y 0 y 1 0 the results of this case follow from the results when b is denoted by i by making a change of variable problems of the form 1 l have been studied by a variety of authors see l 3 5 7 lo 141 for example the most advanced results to date seem to be those in 3 7 and 111 however in these papers f x y is decreasing in y for each x e 0 1 here we will not require this assumption for example we will show that y y o y 0 0 t 1 y 0 y 1 0 with 0 i 2 0 5 y 1 has a solution furthermore in fact in the case where f x y is decreasing in y our results improve those of 3 71 and 111 to show existence of a solution to 1 1 we will use the technique initiated in lo and ll the methods in those papers rely on the topological transversality theorem 8 91 the arzela ascoli theorem and apriori bounds on solutions

correlational kinetics i general theory abstract a kinetic theory for dilute gases with short and long range interactions is derived not only instantaneous but also retarded interactions are considered to treat correlations in an appropriate manner a 2 particle boltzmann density is chosen as the basic quantity of the theory thus the presented theory is the starting point for the derivation of a correlational thermodynamics

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

tangent bundle geometry lagrangian dynamics various aspects of the differential geometry of the tangent bundle of a differentiable manifold are examined and the results applied to time independent lagrangian dynamics it is shown that a certain type 1 1 tensor field which is part of the intrinsic geometry of a tangent bundle being a tensorial equivalent of the projection map of tangent vectors plays a role in lagrangian theory scarcely less important than that of the canonical one form on a cotangent bundle in hamiltonian theory recent results in lagrangian theory are interpreted from this new viewpoint

eigenvalue problems for second order nonlinear dynamic equations on time scales abstract this paper is concerned with the existence and nonexistence of positive solutions of the second order nonlinear dynamic equation 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 we show that there exists a 0 such that the above boundary value problem has at least two one and no positive solutions for 0 and respectively furthermore by using the semiorder method on cones of the banach space we establish an existence and uniqueness criterion for positive solution of the problem in particular such a positive solution u t of the problem depends continuously on the parameter i e u t is nondecreasing in lim 0 u 0 and lim u

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

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

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 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

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

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

numerical methods for unilateral problems abstract the theory of variational inequalities besides being elegant and synthetic also provides a unified general framework for applying the numerical methods for solving many unrelated free boundary value problems in this paper we describe numerical experience on the use of variational inequalities and pade approximants to obtain approximate solutions to a class of unilateral boundary value problems of elasticity like those describing the equilibrium configuration of an elastic beam stretched over an elastic obstacle in the case of a known obstacle these problems can be alternatively formulated as nonlinear boundary value problems without constraints for which the technique of pade approximants can be successfully employed the variational inequality formulation is used to discuss the problem of uniqueness and existence of the solution

multiple positive solutions for some p laplacian boundary value problems this paper deals with the existence of multiple positive solutions for the one dimensional p laplacian f p x t q t f t x t x t 0 t 0 1 subject to the following boundary value conditions x 0 i 1n a ix x i x 1 i 1n b ix x i where f p s s p 2 s p 1 by means of a fixed point theorem due to avery and peterson sufficient conditions are obtained that guarantee the existence of at least three positive solutions to the above boundary value problem

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

existence results for singular three point boundary value problems on time scales abstract we prove the existence of a positive solution for the three point boundary value problem on time scale t given by y f x y 0 x 0 1 t y 0 0 y p y 2 1 where p 0 1 t is fixed and f x y is singular at y 0 and possibly at x 0 y we do so by applying a fixed point theorem due to gatica oliker and waltman j differential equations 79 1989 62 for mappings that are decreasing with respect to a cone we also prove the analogous existence results for the related dynamic equations y f x y 0 y f x y 0 and y f x y 0 satisfying similar three point boundary conditions

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

higher order three point boundary value problem on time scales in this paper we consider a higher order three point boundary value problem on time scales we study the existence of solutions of a non eigenvalue problem and of at least one positive solution of an eigenvalue problem later we establish the criteria for the existence of at least two positive solutions of a non eigenvalue problem examples are also included to illustrate our results

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

existence results for an even order boundary value problem on time scales abstract let t be a time scale with t 1 t 2 t 3 t we investigate the existence of solutions to the nonlinear even order three point boundary value problem 1 n y 2 n t f t y t t t 1 t 3 t y 2 i 1 t 1 0 y 2 i t 3 y 2 i 1 t 3 y 2 i 1 t 2 0 i n 1 where n n t 2 t 1 t 3 0 and 1 are given constants

lagrangian presymplectic constraint analysis of mechanical models of field theories coupled to external fields the lecanda roman roy geometric constraint algorithm for presymplectic lagrangian systems is applied to a mechanical model of singular field theories coupled to time independent external fields the simple yet intrinsic structure of the algorithm allows the influence of the external field to be traced through the constraint analysis showing clearly where pathologies arise namely in the second generation nondynamical constraints arising from the stability of the first generation compatibility constraints using a coordinate independent geometric algorithm provides a more systematic tool for investigating singular field theories than the usual ad hoc manipulation of the field equations where the essential structure is often obscured by the details of the representation of the model and the complexity of the algebra

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

several existence theorems of nonlinear m point boundary value problem for p laplacian dynamic equations on time scales abstract in this paper several existence theorems of positive solutions are established for nonlinear m point boundary value problem for p laplacian dynamic equations on time scales as an application an example to demonstrate our results is given the conditions we used in the paper are different from those in h r sun w t li positive solutions for nonlinear three point boundary value problems on time scales j math anal appl 299 2004 508 524 h r sun w t li positive solutions for nonlinear m point boundary value problems on time scales acta math sinica 49 2006 369 380 in chinese y wang c hou existence of multiple positive solutions for one dimensional p laplacian j math anal appl 315 2006 144 153 y wang w ge positive solutions for multipoint boundary value problems with one dimensional p laplacian nonlinear appl 66 6 2007 1246 1256

a new algorithm for solving dynamic equations on a time scale in this paper we propose a numerical algorithm to solve a class of dynamic time scale equation which is called the q difference equation first we apply the method for solving initial value problems ivps which contain the first and second order delta derivatives illustrative examples show the usefulness of the method then we present applications of the method for solving the strongly non linear damped q difference equation the results show that our method is more accurate than the other existing method

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

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

existence and multiplicity of positive solutions for nonlinear boundary value problems with a parameter in this paper the nonlinear boundary value problem p t u q t email protected t u email protected email protected email protected u 0 u w p 0 u 0 p w u w is studied by using the fixed point index theory some existence multiplicity and nonexistence results for positive solutions are derived in terms of different values of l the results obtained herein generalize and improve the main results of j r graef l kong h wang existence multiplicity and dependence on a parameter for a periodic boundary value problem j differential equations 245 2008 1185 1197 x hao l liu y wu existence and multiplicity results for nonlinear periodic boundary value problems nonlinear anal 72 2010 3635 3642 and some other known results

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

positive solutions and eigenvalue regions of two delay singular systems with a twin parameter abstract the paper is concerned with a two delay singular differential system with a twin parameter applying fixed point index theory we show the relationship between the asymptotic behaviors of nonlinearities at zero and infinity and the open regions eigenvalue regions of parameters which are correlated with delays such that the system has zero one and two positive solution s

some new results on the existence of positive solutions for the one dimensional p laplacian boundary value problems on time scales abstract this paper is devoted to using the leggett williams fixed point theorem to derive some sufficient conditions for the existence of triple positive solutions to a type of p laplacian boundary value problems on time scales the interesting point is that the nonlinear term f depends on the first order delta derivative explicitly

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

boundary value problems occurring in plate deflection theory abstract the paper deals with several iterative methods for solving some boundary value problems occurring in plate deflection theory making it possible to avoid the lengthy problem preparation which is required to solve these problems by finite difference methods

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

existence and multiplicity results for nonlinear boundary value problems this paper studies the existence of positive solutions for a class of boundary value problems of elliptic degenerate equations by using bifurcation and fixed point index theories in the frame of approximation arguments the criteria of the existence multiplicity and nonexistence of positive solutions are established

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