an adaptive non conforming finite element method for reissner mindlin plates adaptive algorithms are important tools for efficient finite element mesh design in this paper an error controlled adaptive mesh refining algorithm is proposed for a non conforming low order finite element method for the reissner mindlin plate model the algorithm is controlled by a reliable and efficient residual based a posteriori error estimate which is robust with respect to the plate s thickness numerical evidence for this and the efficiency of the new algorithm is provided in the sense that non optimal convergence rates are optimally improved in our numerical experiments

fixed point theorems of rothe and altman types about convex power condensing operator and application in this paper fixed point theorems of rothe and altman types about convex power condensing operator are given and applied to the differential equation of one order with integral boundary conditions in abstract space

d split sequences and derived equivalences abstract in this paper we introduce the so called d split sequences and show that each d split sequence gives rise to a derived equivalence via a tilting module in particular we obtain derived equivalences from auslander reiten sequences via bb tilting modules or from n almost split sequences via n bb tilting modules and auslander reiten triangles further we recover n almost split sequences from n bb tilting modules over n auslander algebras

stochastic reaction diffusion equations on networks with dynamic time delayed boundary conditions abstract we consider a reaction diffusion equation on a network subjected to dynamic boundary conditions with time delayed behavior also allowing for multiplicative gaussian noise perturbations exploiting semigroup theory we rewrite the aforementioned stochastic problem as an abstract stochastic partial differential equation taking values in a suitable product hilbert space for which we prove the existence and uniqueness of a mild solution eventually a stochastic optimal control application is studied

optimal constants in a nonlocal boundary value problem we give improved results on the existence of positive solutions for a nonlinear differential equation with nonlocal boundary conditions that arise as a model of a thermostat we obtain some optimal criteria for the existence of one positive solution which involve the principal eigenvalue of a related linear operator we also determine optimal values of some other constants that are useful in obtaining existence of multiple positive solutions

existence and multiplicity of non negative solutions for systems of perturbed hammerstein integral equations abstract we study the existence of positive solutions for a system of perturbed hammerstein integral equations our setting is quite general and covers a wide class of systems of boundary value problems the main ingredient in our theory is the classical fixed point index theory for compact maps

solvability of singular second order m point boundary value problems abstract let f 0 1 r 2 r be a function satisfying caratheodory s conditions and 1 t e t l 1 0 1 let i 0 1 a i r i 1 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a c 1 0 1 solution for the m point boundary value problem x f t x t x t e t 0 t 1 0 1 x 0 0 x 1 i 1 m 2 a i x i the proof of our main result is based upon the leray schauder continuation theorem

recollements from partial tilting complexes abstract we consider recollements of derived categories of differential graded algebras induced by self orthogonal compact objects obtaining a generalization of rickard s theorem specializing to the case of partial tilting modules over a ring we extend the results on triangle equivalences proved in 6 9 in the end we focus on the connection between recollements of derived categories of rings bireflective subcategories and generalized universal localizations

nontrivial solutions of singular nonlinear m point boundary value problems in this paper by using the method of topology degree some existence theorems of nontrivial solutions for singular nonlinear m point boundary value problems are established our nonlinearity may be singular in its dependent variable

nodal solutions for second order m point boundary value problems with nonlinearities across several eigenvalues abstract we study the existence of nodal solutions of the m point boundary value problem u f u 0 0 t 1 u 0 0 u 1 i 1 m 2 i u i where i q i 1 2 m 2 with 0 1 2 m 2 1 and i r i 1 2 m 2 with i 0 and 0 i 1 m 2 i 1 we give conditions on the ratio f s s at infinity and zero that guarantee the existence of nodal solutions the proofs of our main results are based upon bifurcation techniques

existence of changing sign solutions for some semilinear problems with jumping nonlinearities at zero we study the existence of changing sign solutions of an elliptic semilinear boundary value problem which arises as a limiting equation of the two species lotka volterra competing equations system using variational methods and a result of d aujourd hui we find conditions which are both sufficient and necessary for this existence problem

new harnack inequalities and existence theorems for radially symmetric solutions of elliptic pdes with sign changing or vanishing green s function abstract we consider the perturbed hammerstein integral equation y t 1 t h 1 1 y 2 t h 2 2 y 0 1 g t s f s y s d s where 1 and 2 are linear functionals realized as stieltjes integrals with associated signed stieltjes measures we demonstrate that by utilizing a nonstandard order cone together with an associated nonstandard open set existence of a positive solution to the integral equation can be guaranteed under relatively mild hypotheses on the various constituent functions and functionals in the case in which the green s function t s g t s is allowed to both vanish and change sign as an example we apply our results to radially symmetric elliptic pdes of the form u h x g u x x r 1 r 2 r u x x b r 2 0 u r 1 x u r x x b 1 h u where 0 r 1 r r 2 is a linear functional and h is a continuous function as part of this analysis we demonstrate a new methodology for constructing a suitable harnack like inequality associated to the boundary value problem

existence and nonexistence results for positive solutions of an integral boundary value problem abstract this paper deals with the existence and nonexistence of positive solutions for the integral boundary value problem a u b u g t f t u cos 0 u 0 sin 0 u 0 0 1 u d cos 1 u 1 sin 1 u 1 0 1 u d we provide sufficient conditions for the existence of either none or one or more positive solutions of the above problem the main tool used in the proofs of existence results is a fixed point theorem in a cone due to krasnoselskii and zabreiko the results presented substantially unify and extend the existing results in the literature

on sign changing solution for some three point boundary value problems abstract in this paper an existence result of sign changing solution for some three point boundary value problems is obtained by using the fixed point index method

existence of sign changing solutions for some asymptotically linear three point boundary value problems abstract in this paper by using the topological degree theory and the fixed point index theory the existence of three kinds of solutions i e sign changing solutions positive solutions and negative solutions for asymptotically linear three point boundary value problems is obtained

multiplicity results for positive solutions of some semi positone three point boundary value problems in this paper some multiplicity results for positive solutions of some singular semi positone three point boundary value problem be obtained by using the fixed point index method

on sign changing solutions for nonlinear operator equations abstract in this paper the existence of sign changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory the main theorems are some new three solution theorems which are different from the famous amann s and leggett williams three solution theorems as well as the results in f li g han generalization for amann s and leggett williams three solution theorems and applications j math anal appl 298 2004 638 654 these three solutions are all nonzero one of them is positive another is negative and the third one is a sign changing solution furthermore the theoretical results are successfully applied to both integral and differential equations

existence and nonexistence results of impulsive first order problem with integral boundary condition abstract this paper is concerned with a first order impulsive boundary value problem ibvp for short with integral boundary condition and depending on a parameter we obtain the existence and nonexistence results of positive solutions for the ibvp when the nonlinear term and the impulses satisfy different requirements of superlinearity and sublinearity and the parameter lies in some intervals

dual mixed p and hp finite elements for elastic membrane problems a complementary energy based dimensionally reduced plate model using a two field dual mixed variational principle of non symmetric stresses and rotations is derived both the membrane and bending equilibrium equations expressed in terms of non symmetric mid surface stress components are satisfied a priori introducing first order stress functions it is pointed out that i the membrane shear and bending energies of the plate written in terms of first order stress functions are decoupled ii although unmodified 3 d constitutive equations are applied the energy parts do not contain the 1 1 2 term for isotropic linearly elastic materials these facts mean that the finite element formulation based on the present plate model should be free from shear locking when the thickness tends to zero and free from incompressibility locking when the poisson ratio converges to 0 5 irrespective of low order h or higher order p elements are used curvilinear dual mixed hp finite elements with higher order stress approximation and continuous surface tractions are developed and presented for the membrane 2 d elasticity problem in this case the formulation requires the approximation of three independent variables two components of a first order stress function vector and a scalar rotation numerical performance of three quadrilateral dual mixed elements is presented and compared to displacement based hp finite elements when the poisson ratio converges to the incompressible limit of 0 5 the numerical results show that as expected the dual mixed elements developed in this paper are free from locking in the energy norm as well as in the stress computations for both h and p extensions copyright 2001 john wiley sons ltd

on the existence of positive solution for second order multi points boundary value problems here we are concerned with the existence of positive solution for autonomous and nonautonomous second order systems with multi points boundary conditions for nonautonomous systems we use the schauder s fixed point theorem in a suitable banach space while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree in order to verify the obtained results we have considered some definite systems to verify the results numerically

sign changing solutions to second order integral boundary value problems abstract in this paper by using the fixed point index theory and leray schauder degree theory we consider the existence and multiplicity of sign changing solutions to nonlinear second order integral boundary value problem u t f u t for all t 0 1 subject to u 0 0 and u 1 g 0 1 u s d s where f g c r r we obtain some new existence results concerning sign changing solutions by computing hardly eigenvalues and the algebraic multiplicities of the associated linear problem if f and g satisfy certain conditions then this problem has at least six different nontrivial solutions two positive solutions two negative solutions and two sign changing solutions moreover if f and g are also odd then the problem has at least eight different nontrivial solutions which are two positive two negative and four sign changing solutions

localization of triangulated categories and derived categories the notion of quotient and localization of abelian categories by dense subcategories i e serre classes was introduced by gabriel and plays an important role in ring theory 6 131 the notion of triangulated categories was introduced by grothendieck and developed by verdier 9 16 and is recently useful in representation theory 8 4 143 the quotient of triangulated categories by epaisse subcategories is constructed in 16 both quotients were indicated by grothendieck and they resemble each other in this paper we will consider triangulated categories and derived categories from the point of view of localization of abelian categories verdier gave a condition which is equivalent to the one that a quotient functor has a right adjoint and considered a relation between tpaisse subcategories 16 we show that localization of triangulated categories is similarly defined and have a relation between localizations and cpaisse subcategories beilinson bernstein and deligne introduced the notion of t structure which is similar to torsion theory in abelian categories 2 we in particular consider a stable t structure which is an epaisse subcategory and deal with a correspondence between localizations of triangulated categories and stable r structures and then recollement in the sense of 2 is equivalent to bilocalization next we show that quotient and localization of abelian categories induce quotient and localization of its derived categories in section 1 we recall standard notations and terminologies of quotient and localization of abelian categories in section 2 we define localization of triangulated categories and consider a relation between localizations and stable r structures theorem 2 6 in section 3 we show that if a a c is a quotient of abelian categories then d a d a c is a quotient of triangulated categories where or b theorem 3 2 moreover

derived equivalences induced by big cotilting modules abstract we prove that given a grothendieck category g with a tilting object of finite projective dimension the induced triangle equivalence sends an injective cogenerator of g to a big cotilting module moreover every big cotilting module can be constructed like that in an essentially unique way we also prove that the triangle equivalence is at the base of an equivalence of derivators which in turn is induced by a quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes

a uniformly accurate finite element method for the reissner mindlin plate a simple finite element method for the reissner mindlin plate model in the prim itive variables is presented and analyzed the method uses nonconforming linear finite elements for the transverse displacement and conforming linear finite elements enriched by bubbles for the rotation with the computation of the element stiffness matrix modified by the inclusion of a simple elementwise averaging it is proved that the method converges with optimal order uniformly with respect to thickness

robust bddc preconditioners for reissner mindlin plate bending problems and mitc elements a balancing domain decomposition method by constraints bddc is constructed and analyzed for the reissner mindlin plate bending problem discretized with mixed interpolation of tensorial components mitc finite elements this bddc algorithm is based on selecting the plate rotations and deflection degrees of freedom at the subdomain vertices as primal continuity constraints after the implicit elimination of the interior degrees of freedom in each subdomain the resulting plate schur complement is solved by the preconditioned conjugate gradient method the preconditioner is based on the solution of local reissner mindlin plate problems on each subdomain with clamping conditions at the primal degrees of freedom and on the solution of a coarse reissner mindlin plate problem for the primal degrees of freedom the main results of the paper are the proof and numerical verification that the proposed bddc plate algorithm is scalable quasi optimal and most important robust with respect to the plate thickness while this result is due to an underlying mixed formulation of the problem both the interface plate problem and the preconditioner are positive definite the numerical results also show that the proposed algorithm is robust with respect to discontinuities of the material properties

solutions and green s functions for some linear second order three point boundary value problems in this paper we consider the green s functions for a second order linear ordinary differential equation with some three point boundary conditions we give exact expressions of the unique solutions for the linear three point boundary problems by the green s functions as applications we study the iterative solutions for some nonlinear singular second order three point boundary value problems

existence of nontrivial periodic solutions for a nonlinear second order periodic boundary value problem abstract in this paper we study the existence of nontrivial periodic solutions to the following nonlinear differential equation u t a t u t f t u t t r u 0 u u 0 u where a r r is an periodic continuous function with a t 0 f r r r is continuous may take negative values and can be sign changing without making any nonnegative assumption on nonlinearity by using the first eigenvalue corresponding to the relevant linear operator and the topological degree the existence of nontrivial periodic solutions to the above periodic boundary value problem is established finally three examples are given to demonstrate the validity of our main results

analysis of the discontinuous petrov galerkin method with optimal test functions for the reissner mindlin plate bending model we analyze the discontinuous petrov galerkin dpg method with optimal test functions when applied to solve the reissner mindlin model of plate bending we prove that the hybrid variational formulation underlying the dpg method is well posed stable with a thickness dependent constant in a norm encompassing the l 2 norms of the bending moment the shear force the transverse deflection and the rotation vector we then construct a numerical solution scheme based on quadrilateral scalar and vector finite elements of degree p we show that for affine meshes the discretization inherits the stability of the continuous formulation provided that the optimal test functions are approximated by polynomials of degree p 3 we prove a theoretical error estimate in terms of the mesh size h and polynomial degree p and demonstrate numerical convergence on affine as well as non affine mesh sequences

a classification theorem for t structures abstract we give a classification theorem for a relevant class of t structures in triangulated categories which includes in the case of the derived category of a grothendieck category a large class of t structures whose hearts have at most n fixed consecutive non zero cohomologies moreover by this classification theorem we deduce the construction of the t tree a new technique which generalizes the filtration induced by a torsion pair at last we apply our results in the tilting context generalizing the 1 tilting equivalence proved by happel reiten and smalo 16 the last section provides applications to classical n tilting objects examples of t trees for modules over a path algebra and new developments on compatible t structures 22 20

the sign changing solutions for nonlinear elliptic problem with carrier type abstract in this paper using the fixed point index method we are concerned with the existence of sign changing solutions of the following problem 0 1 a b u x d x u f u x in u x 0 x on where a 0 b 0 and r n is a bounded open set with smooth boundary and 1

optimal existence criteria for symmetric positive solutions to a three point boundary value problem abstract in this paper we shall consider the following second order three point boundary value problem u t a t f t u t 0 0 t 1 u 0 u 1 u where 0 1 0 1 2 a l 1 0 1 is nonnegative and symmetric on 0 1 f 0 1 0 0 satisfies caratheodory conditions and f u is symmetric on 0 1 for all u 0 by using fixed point index theorems we get some optimal existence criteria for the existence of one or two symmetric solutions which involve the principal eigenvalue of a related linear operator

upper and lower error bounds for plate bending finite elements we compare the robustness of three different low order mixed methods that have been proposed for plate bending problems the so called mitc arnold falk and arnold brezzi elements we show that for free plates the asymptotic rate of convergence in the presence of quasiuniform meshes approaches the optimal o h for mitc elements as the thickness approaches 0 but only approaches o h frac 1 2 for the latter two we accomplish this by establishing lower bounds for the error in the rotation the deterioration occurs due to a consistency error associated with the boundary layer we show how a modification of the elements at the boundary can fix the problem finally we show that the arnold brezzi element requires extra regularity for the convergence of the limiting discrete kirchhoff case and show that it fails to converge in the presence of point loads

nontrivial solutions of singular sublinear sturm liouville problems abstract the singular superlinear sturm liouville problems l x h x f x 0 x 1 r 1 1 0 1 0 0 r 2 2 1 2 1 0 are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators where l x p x x q x x and h x is allowed to be singular at both x 0 and x 1 in particular f is not necessary to be nonnegative the existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory

a sharper condition for the solvability of a three point second order boundary value problem letf 0 1 r2 rbe a function satisfying caratheodory s conditions ande t l1 0 1 let 0 1 r 1 1 be given this paper is concerned with the problem of existence of a solution for the three point boundary value problem formula omitted this problem was studied earlier by gupta ntouyas and tsamatos when 1 and when 1 with 1 in the general case this problem was studied by gupta as a multi point boundary value problem in this paper sharper existence conditions are obtained for the solvability of the above boundary value problem in the general case

on the heart of a faithful torsion theory abstract in r colpi k r fuller tilting objects in abelian categories and quasitilted rings trans amer math soc in press tilting objects in an arbitrary abelian category h are introduced and are shown to yield a version of the classical tilting theorem between h and the category of modules over their endomorphism rings moreover it is shown that given any faithful torsion theory x y in mod r for a ring r the corresponding heart h x y is an abelian category admitting a tilting object which yields a tilting theorem between the heart and mod r in this paper we first prove that h x y is a prototype for any abelian category h admitting a tilting object which tilts to x y in mod r then we study ab type properties of the heart and commutations with direct limits this allows us to show for instance that any abelian category h with a tilting object is ab4 and to find necessary and sufficient conditions which guarantee that h is a grothendieck or even a module category as particular situations we examine two main cases when x y is hereditary cotilting proving that h x y is grothendieck and when x y is tilting proving that h x y is a module category

existence of nontrivial solutions for a nonlinear sturm liouville problem with integral boundary conditions abstract this paper deals with the existence of nontrivial solutions for a nonlinear singular sturm liouville problem with integral boundary conditions

solvability of an m point boundary value problem for second order ordinary differential equations let 0 1 r2 r be a function satisfying caratheodory s conditions and e t l1 0 1 let i 0 1 ai r all of the ai s having the same sign i 1 2 m 2 0 1 2 m 2 1 be given this paper is concerned with the problem of existence of a solution for the m point boundary value problem x t t x t x t e t t 0 1 e formula conditions for the existence of a solution for the above boundary value problem are given using the leray schauder continuation theorem

closed subbifunctors of the extension functor abstract given a subbifunctor f of ext 1 one can ask if one can generalize the construction of the derived category to obtain a relative derived category where one localizes with respect to f acyclic sequences we show that this is possible if and only if f is closed we also show that for artin algebras the closed subbifunctors correspond to serre subcategories of a category of finitely presented functors that vanish on projectives and we use this to find new examples of closed subbifunctors using relatively derived categories we give a relative version of happel s result on derived equivalences induced by tilting and we show in an example how this can be used to find ordinary derived equivalences

positive solutions to a type of nonlinear three point boundary value problem with sign changing nonlinearities in this paper by using krasnoselskii s fixed point theorem in a cone we study the existence of positive solutions for the second order three point boundary value problem u t a t u t lf t u t 0 0

on sign changing solutions for a second order integral boundary value problem in this paper we obtain the existence of sign changing solutions for nonlinear second order differential equations with integral boundary value conditions by applying a new fixed point theorem in ordered banach spaces with the lattice structure derived by liu and sun our results improve on those in the literature

on an m point boundary value problem for second order ordinary differential equations where q e 0 1 is given we obtain conditions for the existence and uniqueness of a solution for the boundary value problem 2 using the leray schauder continuation theorem 2 we give an example of a three point boundary value problem where the existence condition is not satisfied and no solution exists gupta 3 recently studied the boundary value problem 2 when q 1 our results on the three point boundary value problem 2 extend the results of gupta 3 to the case of general cy see also 4 51 we use the classical spaces c o 11 c o 11 lk o 11 and l o l of continuous k times continuously differentiable measurable real valued functions whose kth power of the absolute value is lebesgue integrable on 0 11 or measurable functions that are essentially bounded

eigenvalues of semi positone hammerstein integral equations and applications to boundary value problems eigenvalue intervals and the existence of finitely many positive eigenfunctions for semi positone hammerstein integral equations are obtained the positive characteristic values and their upper and lower bounds of the corresponding linear hammerstein integral operators are studied applications of the results are given to third order differential equations with three point boundary conditions

the first locking free plane elastic finite element historia mathematica abstract we consider a two parameter family of conforming bilinear quadrilateral finite element formulations for plane elastic problems with homogeneous isotropic material the approach taken earlier by belytschko et al is based on numerical strain reductions and stabilization and may be viewed as an extension reformulation of the classical turner rectangle of 1956 we present the full theory of this approach in the energy norm framework the analysis is based on splitting the error in two orthogonal components the approximation error and the equilibrium or consistency error the theory covers the full parametric dependence of the plane elastic problem emphasizing in particular the case of beam like bodies with arbitrarily small aspect ratios the theory shows that depending on the mesh the stabilized reduced strain formulation is capable of avoiding some or even all the parametric locking effects characteristic to 2d elastic problems we analyze first these locking effects in the context of standard bilinear fem

on nonlinear boundary conditions satisfying certain asymptotic behavior abstract in this paper we consider a second order boundary value problem of the form y t a t g y t y 0 y y 1 0 we demonstrate that if the nonlinear functional y satisfies certain asymptotic behavior then the problem will possess at least one positive solution these results generalize and improve on some recent results in the literature on boundary value problems with nonlocal nonlinear boundary conditions and we provide some examples which illustrate these generalizations and improvements

gorenstein defect categories of triangular matrix algebras abstract we apply the technique of recollement to study the gorenstein defect categories of triangular matrix algebras first we construct a left recollement of gorenstein defect categories for a triangular matrix algebra under some conditions using it we give a categorical interpretation of the gorenstein properties of the triangular matrix algebras obtained by x w chen b l xiong and p zhang respectively second under some additional conditions a recollement of gorenstein defect categories for a triangular matrix algebra is constructed as an application for a special kind of triangular matrix algebras which are called simple gluing algebras we describe their singularity categories and gorenstein defect categories

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

multiplicity of sign changing solutions for some four point boundary value problem abstract in this paper we obtain using leray schauder degree theory some multiplicity results for sign changing solutions of a four point boundary value problem we assume the existence of a pair of strict lower and upper solutions and some additional conditions on the nonlinear term f

existence of positive negative and sign changing periodic solutions for a class of integral equations in this paper the simultaneous existence of positive negative and sign changing periodic solutions for a class of integral equations of the form f x email protected x x w wk x y f y f email protected y dy email protected email protected is considered where w is a closed subset of r n with a periodic structure our main result is different from most existing results since they provide three constant sign periodic solutions only

three nonnegative solutions for fractional differential equations with integral boundary conditions in this paper we study multiple nonnegative solutions for the fractional differential equation with integral boundary conditions cd ax t f t x t 0 email protected 0 1 x 0 email protected 0 1g 0 s x s ds x 1 email protected 0 1g 1 s x s ds x k 0 email protected 0 1g k s x s ds k 2 3 a by means of leggett williams fixed point theorem some new results on the existence of at least three nonnegative solutions are obtained

on faithfully balanced modules f cotilting and f auslander algebras abstract the aim of this paper is to give a unification of the theory of co tilting modules and higher auslander correspondence by using faithfully balanced modules i e faithful modules with the double centralizer property in the language of relative homological algebra following auslander solberg a relative version of faithfully balancedness is given which will be called 1 f faithful the relative versions of higher auslander correspondence and brenner butler theorem are also developed

positive solutions for singular m point boundary value problems with positive parameter in this paper some new existence results for positive solutions for a class of singular m point boundary value problems with parameter be obtained

nontrivial solutions of singular two point boundary value problems with sign changing nonlinear terms abstract the singular two point boundary value problem u t h t f u t t 0 1 u 0 u 1 0 is considered under some conditions concerning the first eigenvalue corresponding to the relevant linear problem where h is allowed to be singular at both t 0 and t 1 moreover f is a sign changing function and not necessarily bounded from below by computing the topological degree of an completely continuous field the existence results of nontrivial solutions are established