deformations of quasi homogeneous surface singularities let a a be a finitely generated normal graded domain over e so that i 0 v spec a has an isolated singularity we say v is a quasi homogeneous singularity or admits a good ie action or is defined by weighted homogeneous polynomials we are concerned with two questions about the deformations of v there are two natural notions of equisingular deformation of v first one has deformations of weight 0 that is one perturbs the defining equations of vby terms of weight at least as big to make a good notion out of this dock sang rim observed one is really deforming a and the weight filtration ij where ij ai

degree theory for s mappings in non reflexive banach spaces abstract let e be a real banach space e the dual space of e e the dual space of e and e an open bounded subset and let t 2 e be a weak compact mapping of class s see definition 1 2 we will construct a degree theory for such a mapping

degree of mapping for nonlinear mappings of monotone type abstract a classical degree function is constructed for pseudomonotone mappings from a reflexive banach space to its dual using galerkin approximations this generalizes the leray schauder degree when the banach space is a hilbert space and yields a flexible analytical tool for the study of nonlinear elliptic problems of higher order in divergence form

factorization of minty and stampacchia variational inequality systems abstract in this paper sufficient regularity and coercivity conditions for minty and stampacchia type variational inequality systems are offered the typical results state that if the independent inequalities are solvable and the functions involved are lower semicontinuous then the system has also a solution that is a factorization principle holds as an application a variational inequality system consisting of two partial differential inequalities is considered this result is analogous to that of chen journal of mathematical analysis and application 231 1999 177 obtained for one variational inequality

quasistatic normal compliance contact problem of visco elastic bodies with coulomb friction implemented by qp and sgbem the quasistatic normal compliance contact problem of isotropic homogeneous linear visco elastic bodies with coulomb friction at small strains in kelvin voigt rheology is considered the discretization is made by a semi implicit formula in time and the symmetric galerkin boundary element method sgbem in space assuming that the ratio of the viscosity and elasticity moduli is a given relaxation time coefficient the obtained recursive minimization problem formulated only on the contact boundary has a nonsmooth cost function if the normal compliance responds linearly and the 2d problems are considered then the cost function is piecewise quadratic which after a certain transformation gets the quadratic programming qp structure however it would lead to second order cone programming in 3d problems finally several computational tests are presented and analysed with an additional discussion on numerical stability and convergence of the involved approximated poincare steklov operators

a multiplicity theorem for problems with the p laplacian abstract we consider nonlinear elliptic equations driven by the p laplacian differential operator using degree theoretic arguments based on the degree map for operators of type s we prove the existence of two nontrivial smooth solutions one of which is of constant sign

on pseudomonotone set valued mappings abstract in this paper a common generalization of the algebraic and topological pseudomonotonicity for set valued maps is introduced existence results for variational inequalities governed by such maps are given

nonresonance conditions for generalised ϕ laplacian problems with jumping nonlinearities abstract we consider the boundary value problem 0 1 x u x u x f x u x u x a e x 0 1 0 2 c 00 u 0 c 01 u 0 c 10 u 1 c 11 u 1 where c j 0 c j 1 0 for each j 0 1 and f 0 1 r 2 r are caratheodory functions with suitable additional properties the differential operator generated by the left hand side of 0 1 together with the boundary conditions 0 2 is a generalisation of the usual p laplacian and also of the so called laplacian which corresponds to x s t t with an odd increasing homeomorphism for the p laplacian problem and more particularly the semilinear case p 2 nonresonance conditions which ensure the solvability of the problem 0 1 0 2 have been obtained in terms of either eigenvalues for non jumping f or the fucik spectrum or half eigenvalues for jumping f of the p laplacian in this paper under suitable growth conditions on and f we extend these conditions to the general problem 0 1 0 2

a variational inequality theory in reflexive smooth banach spaces and applications to p laplacian elliptic inequalities abstract we develop a theory of variational inequality for demicontinuous s contractive maps in reflexive smooth banach spaces variational inequality theorems are proved and applied to study existence of nonzero positive weak solutions for p laplacian elliptic inequalities and a population model of one species arising in mathematical biology

on the degree theory for general mappings of monotone type degree theory has been developed as a tool for checking the solution existence of nonlinear equations in his classic paper published in 1983 browder developed a degree theory for mappings of monotone type f t w heref is a mapping of class s from a bounded open set in a reflexive banach space x into its dual x a ndt is a maximal monotone mapping from x into x this breakthrough paved the way for many applications of degree theoretic techniques to several large classes of nonlinear partial differential equations in this paper we continue to develop the results of browder on the degree theory for mappings of monotone type f t by enlarging the class of maximal monotone mappings and pseudo monotone homotopies we obtain some new results of the degree theory for such mappings 2007 elsevier inc all rights reserved

strongly quasibounded maximal monotone perturbations for the berkovits mustonen topological degree theory abstract let x be a real reflexive banach space with dual x let l x d l x be densely defined linear and maximal monotone let t x d t 2 x with 0 d t and 0 t 0 be strongly quasibounded and maximal monotone and c x d c x bounded demicontinuous and of type s w r t d l a new topological degree theory has been developed for the sum l t c this degree theory is an extension of the berkovits mustonen theory for t 0 and an improvement of the work of addou and mermri for t x 2 x bounded unbounded maximal monotone operators with 0 d t are strongly quasibounded and may be used with the new degree theory

on the semi monotone operator theory and applications abstract in this paper eis a real banach space a e e e is a semi monotone operator we first study the variational inequality problem findu k such that a u u v u 0 wherek e is a closed convex subset then the operator equationa u u p and we also construct a degree theory for demi continuous semi monotone operators in reflexive banach spaces

nonlinear second order differential inclusions with a series of convex functions abstract in this paper we study a class of second order differential inclusions attached to which the convex potential varies depending on the time and the boundary conditions are described by the subdifferentials of convex functions applying the theory of lower semicontinuous convex and proper functionals and fixed points we give some results about the representation of the subdifferential operators of some convex functionals and the existence of solutions for the boundary value problems

extension of the leray schauder degree for abstract hammerstein type mappings abstract we introduce a new extension of the classical leray schauder topological degree in a real separable reflexive banach space the new class of mappings for which the degree will be constructed is obtained essentially by replacing the compact perturbation by a composition of mappings of monotone type it turns out that the class contains the leray schauder type maps as a proper subclass the new class is not convex thus preventing the free application of affine homotopies however there exists a large class of admissible homotopies including subclass of affine ones so that the degree can be effectively used we shall construct the degree and prove that it is unique we shall generalize the borsuk theorem of the degree for odd mappings and show that the principle of omitted rays remains valid to illuminate the use of the new degree we shall briefly consider the solvability of abstract hammerstein type equations and variational inequalities

dynamic stress concentration studies by boundary integrals and laplace transform the dynamic stress field and its concentrations around holes of arbitrary shape in infinitely extended bodies under plane stress or plane strain conditions are numerically determined the material may be linear elastic or viscoelastic while the dynamic load consists of plane compressional waves of harmonic or general transient nature the method consists of applying the laplace transform with respect to time to the governing equations of motion and formulating and solving the problem numerically in the transfomed domain by the boundary integral equation method the stress field can then be obtaind by a numerical inversion of the trasformed solution the correspondence principle is invoked for the case of viscoelastic material behavious the method is simplified for the case of harmonic waves where no numerical inversion is involved

an incremental relaxation finite element analysis of viscoelastic problems with contact and friction abstract based on the principle of virtual work a general but effective finite element technique associated with an incremental relaxation procedure is established for the analysis of viscoelastic contact problems with friction a generalized maxwell model is used to model the viscoelastic constitutive equations of which the relaxation function is represented by the sum of a series of decaying exponential functions of time the contact behaviors are accurately performed through a transformation matrix method by the incremental relaxation procedure developed the stress of each element of the generalized maxwell model at instant t n 1 includes two parts 1 the part decaying from the stress at instant t n during the time interval t n t n 1 and 2 the incremental stress induced from the incremental strain applied at instant t n the total stress at instant t n 1 can thus be computed by the sum of the stress of the elements of the generalized maxwell model and is only dependent on the previous stress level and the incremental strain applied at instant t n hence both the total strain and displacement at each instant are not used in the total stress calculation in addition the numerical errors caused by selecting larger time increments can also be avoided finally the influence of friction on the contact traction distributed on the contact surface at various time instants is presented

a simple and efficient bem implementation of quasistatic linear visco elasticity abstract a simple yet efficient procedure to solve quasistatic problems of special linear visco elastic solids at small strains with equal rheological response in all tensorial components utilizing boundary element method bem is introduced this procedure is based on the implicit discretisation in time the so called rothe method combined with a simple algebraic transformation of variables leading to a numerically stable procedure proved explicitly by discrete energy estimates which can be easily implemented in a bem code to solve initial boundary value visco elastic problems by using the kelvin elastostatic fundamental solution only it is worth mentioning that no inverse laplace transform is required here the formulation is straightforward for both 2d and 3d problems involving unilateral frictionless contact although the focus is to the simplest kelvin voigt rheology a generalization to maxwell boltzmann jeffreys and burgers rheologies is proposed discussed and implemented in the bem code too a few 2d and 3d initial boundary value problems one of them with unilateral frictionless contact are solved numerically

topological degree theories and nonlinear operator equations in banach spaces abstract let x be a real banach space and g 1 g 2 two nonempty open and bounded subsets of x such that 0 g 2 and g 2 g 1 the problem t x c x 0 is considered where t x d t x or x is an accretive or monotone operator with 0 d t and t 0 0 while c x d c x or x can be e g one of the following types a compact b continuous and bounded with the resolvents of t compact c demicontinuous bounded and of type s with t positively homogeneous of degree one d quasi bounded and satisfying a generalized s condition w r t the operator t while t is positively homogeneous of degree one solutions are sought for the problem lying in the set d t c g 1 g 2 these solutions are nontrivial even when c 0 0 the degree theories of leray and schauder browder and skrypnik are used as well as the degree theory by kartsatos and skrypnik for densely defined operators t c the last three degree theories do not assume any compactness conditions the excision and additivity properties of these degree theories are employed and the main results are significant extensions or generalizations of previous results by krasnoselskii guo ding and kartsatos and other authors involving the relaxation of compactness conditions and or conditions on the boundedness of the operator t an application in the field of partial differential equations is also included

generalized vector complementarity type problems in topological vector spaces in this paper we introduced the generalized vector variational inequality type problem and the generalized vector complementarity type problem in the setting of topological vector space by utilizing a modified version of the fan kkm theorem we investigated the nonemptyness and compactness of solution sets of these problems without the demipseudomonotonicity assumption further we prove that solution sets of both the problems are equivalent to each other under some suitable conditions the results of this paper generalize and improve several results that appeared recently in the literature

positive weak solutions of semilinear second order elliptic inequalities via variational inequalities existence uniqueness and convergence of approximants of positive weak solutions for semilinear second order elliptic inequalities are obtained the nonlinearities involved in these inequalities satisfy suitable upper or lower bound conditions or monotonicity conditions the lower bound conditions are allowed to contain the critical sobolev exponents the methodology is to establish variational inequality principles for demicontinuous pseudo contractive maps in hilbert spaces by considering convergence of approximants and apply them to the corresponding variational inequalities arising from the semilinear second order elliptic inequalities examples on the existence uniqueness and convergence of approximants of positive weak solutions of the semilinear second order elliptic inequalities are given

fixed point theory and nonlinear problems introduction among the most original and far reaching of the contributions made by henri poincare to mathematics was his introduction of the use of topological or qualitative methods in the study of nonlinear problems in analysis his starting point was the study of the differential equations of celestial mechanics and in particular of their periodic solutions his work on this topic began with his thesis in 1879 and was developed in detail in his great three volume work methodes nouvelles de la mechanique celeste which appeared in the early 1890s and summarized his many memoirs of the intervening period it continued until his memoir shortly before his death in 1912 in which he put forward the unproved fixed point result usually referred to as poincare s last geometric theorem the ideas introduced by poincare include the use of fixed point theorems the continuation method and the general concept of global analysis the writer s acquaintance with poincare s influence came through contact with solomon lefschetz and marston morse both of whom were very explicit as to the role of poincare as an initiator in this direction of mathematical development in 1934 in the foreword to his colloquium volume on the calculus of variations in the large morse had put this forward very forcefully in the first paragraph

a new topological degree theory for densely defined s l perturbations of multivalued maximal monotone operators in reflexive separable banach spaces abstract let x be a real reflexive separable locally uniformly convex banach space with locally uniformly convex dual space x let t x d t 2 x be maximal monotone with 0 d t and 0 t 0 and c x d c x assume that l d c is a dense linear subspace of x c is of class s l and c x x x x d c where r r is nondecreasing a new topological degree theory is developed for the sum t c the current approach utilizes the approximate degree d t t c g 0 t 0 t t t 1 t j 1 1 g x open and bounded of kartsatos and skrypnik for the single valued mapping t t c the subdifferential for belonging to a large class of proper convex lower semicontinuous functions gives rise to operators t to which this degree theory applies a theoretical application to an existence problem of nonlinear analysis is included

bernstein nagumo conditions and solutions to nonlinear differential inequalities abstract for an open bounded subset of r n with smooth boundary and 1 p we establish w 1 p a priori bounds and prove the compactness of solution sets to differential inequalities of the form div a x u f x u u which are bounded in l the main point in this work is that the nonlinear term f may depend on u and may grow as fast as a power of order p in this variable such growth conditions have been used extensively in the study of boundary value problems for nonlinear ordinary differential equations and are known as bernstein nagumo growth conditions in addition we use these results to establish a sub supersolution theorem

on the existence of periodic solutions for nonlinear evolutions in hilbert spaces a periodic solutions for nonlinear evolution equations of the form du dt au t f t u t t r where f r h 2 is a set valued caratheodory function are considered when both f and a are set valued mappings and not necessarily linear

topological degree for s mappings with maximal monotone perturbations and its applications to variational inequalities abstract this paper is concerned with the topological degree for mappings of class s with maximal monotone perturbations several results and remarks concerning the evaluation of this degree are given in particular it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one as applications two examples of elliptic variational inequalities are given where the multiple existence of solutions is discussed

boundary integral equation method for general viscoelastic analysis from basic assumptions of viscoelastic constitutive relations and weight residual techniques a boundary element procedure is achieved for both kelvin and boltzmann models imposing spatial approximations and adopting convenient kinematical relations for strain velocities a system of time differential equations is achieved this system is solved adopting linear approximations for displacements resulting in a time marching methodology this approach avoids the use of relaxation functions and makes easier changes in boundary conditions along time natural or essential an important feature of the resulting technique is the absence of domain discretizations which simplify the treatment of problems involving infinite domains tunnels and cavities inside the soil some examples are shown in order to demonstrate the accuracy and stability of the technique when compared to analytical solutions

on the generalized monotonicity of variational inequalities in this paper three new classes of generalized monotone operators are introduced the relaxed m pseudomonotone operator relaxed m quasimonotone operator and densely relaxed pseudomonotone operator the relations between these three classes and the relations between them and some other well known classes of generalized monotone operators are discussed in detail various existence results for variational inequalities in normed spaces are derived the results generalize some known results

generalized mixed equilibrium problems with generalized α η monotone bifunction in topological vector spaces the purpose of this paper is to introduce a new class of the generalized mixed equilibrium problems with a new definition of the relaxed monotonicity for bi functions in topological vector spaces by employing the kkm technique and under some appropriate assumptions on the considering nonlinear mappings we obtain the existence of a solution for the generalized mixed equilibrium problems with the new concept of the relaxed monotonicity and coercivity condition in order to relax the compactness of the domains of the nonlinear mappings in the setting of topological vector spaces moreover the compactness and convexness of the solution set are investigated the results in the paper extend and generalize the corresponding results especially sintunavarat 2013 20 in this area by providing mild assumptions in order to guarantee the existence of a solution for the generalized mixed equilibrium problem

application of high order quadrature rules to time domain boundary element analysis of viscoelasticity this paper presents an accurate and efficient method for the treatment of time integrals in time domain boundary integral equations for viscoelastic problems first the integral equations in space and time are derived for linear viscoelastic and thermo viscoelastic problems then various quadrature rules are discussed for the computation of time integrals a modified simpson s rule is proposed as an effective integration scheme the proposed procedure requires a small computational effort and it is applicable even in time domain boundary element analysis of many different problems numerical results of example problems show the accuracy and effectiveness of the proposed method

limit cycles of discontinuous piecewise polynomial vector fields abstract when the first average function is non zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x y x 2 y 2 2 m and y x x 2 y 2 2 m with m 1 when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces the positive integers m n and k are arbitrary the main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields

a new topological degree theory for perturbations of the sum of two maximal monotone operators abstract let x be an infinite dimensional real reflexive banach space with dual space x and g x open and bounded assume that x and x are locally uniformly convex let t x d t 2 x be maximal monotone and strongly quasibounded s x d s x maximal monotone and c x d c x strongly quasibounded w r t s and such that it satisfies a generalized s condition w r t s assume that d s l d t d c where l is a dense subspace of x and 0 t 0 s 0 0 a new topological degree theory is introduced for the sum t s c with degree mapping d t s c g 0 the reason for this development is the creation of a useful tool for the study of a class of time dependent problems involving three operators this degree theory is based on a degree theory that was recently developed by kartsatos and skrypnik just for the single valued sum s c as above

a generalized vector variational inequality problem with a set valued semi monotone mapping abstract in this paper we first generalize the concept of semi monotonicity for a scalar single valued mapping to the case of a vector set valued mapping then we consider a generalized vector variational inequality problem concerning the vector set valued semi monotone mapping several existence results are obtained by using the kakutani fan glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years

existence of periodic solutions for first order evolution equations without coercivity abstract in this paper we study the existence problem of periodic solutions for the following first order nonlinear evolution equation u t a t u t f t u t 0 t r u t t u t t r in a hilbert space h where a is a monotone type operator and f is a nonlinear operator existence results are obtained without assuming the coercivity condition

generalizations of browder s degree theory the starting point of this paper is the recent important work of f e browder who extended degree theory to operators of monotone type the degree function of browder is generalized to maps of the form t f g where t is maximal monotone f is of class s bounded and g is an u s c compact multifunction it is also generalized to maps of the form f ng with f of class s and ng the nemitsky operator of a multifunction g x r satisfying various types of sign conditions some examples are also included to illustrate the abstract results

degree theory for generalized variational inequalities and applications in this paper a degree theory for finite dimensional generalized variational inequalities is built and employed to prove some results on solution existence and solution stability

a generalized mixed vector variational like inequality problem abstract in this paper we introduce relaxed p monotone mapping and by utilizing kkm technique and nadler s lemma we establish some existence results for the generalized mixed vector variational like inequality problem further we give the concepts of complete semicontinuity and strong semicontinuity and prove the solvability for generalized mixed vector variational like inequality problem without monotonicity assumption by applying the brouwer s fixed point theorem the results presented in this paper are extensions and improvements of some earlier and recent results in the literature

equilibrium problems with set valued mappings in banach spaces abstract in this paper we consider two classes of equilibrium problems which imply general pseudomonotonicity and general semipseudomonotonicity relative to a set valued map on reflexive and nonreflexive banach spaces respectively using the classical kkm technique we obtain some existence results under boundedness as well as under unboundedness assumptions some examples are given

existence results for stampacchia and minty type implicit variational inequalities with multivalued maps abstract stampacchia and minty type generalized implicit variational inequality problems are considered we extended the notion of dense pseudomonotonicity for multivalued maps and established several existence results for solutions of these problems in the setting of segment dense sets we also studied the existence of solutions of minty type generalized implicit quasi variational inequality problems some particular cases are also studied it is shown that our results contain several existing results in the literature as special cases

the bolzano mean value theorem and partial differential equations abstract we study the existence of solutions to abstract equations of the form 0 a u f u u k e where a is an abstract differential operator acting in a banach space e k is a closed convex set of constraints being invariant with respect to resolvents of a and a perturbation f satisfies a certain tangency condition such problems are closely related to the so called poincare miranda theorem being the multi dimensional counterpart of the celebrated bolzano intermediate value theorem in fact our main results should be regarded as infinite dimensional variants of bolzano and miranda poincare theorems along with single valued problems we deal with set valued ones yielding the existence of the so called constrained equilibria of set valued maps the abstract results are applied to show existence of strong steady state solutions to some weakly coupled systems of drift reaction diffusion equations or differential inclusions of this type in particular we get the existence of strong solutions to the dirichlet neumann and periodic boundary problems for elliptic partial differential inclusions under the presence of state constraints of different type certain aspects of the bernstein theory for bvp for second order ode are studied too no assumptions concerning structural coupling monotonicity cooperativity are undertaken

on the removal of rigid body motions in the solution of elastostatic problems by direct bem a theoretical and numerical study of the removal of rigid body motions in the solution of the boundary form of somigliana identity and of the corresponding discretized linear system of the direct bem is presented this study is based on the fredholm theory of linear operators and mechanical aspects of the problem various methods suitable for implementation in bem codes are analyzed and relations between apparently different methods are shown the relation between global equilibrium conditions and solvability of the discretized linear system of the direct bem is discussed

existence and multiplicity results for some quasilinear elliptic equation with weights using variational methods we show the existence and multiplicity of solutions of singular boundary value problems of the type div x a u u x f x u in u 0on where the numbers and as well as the functions a and f satisfy certain conditions

on the normalized eigenvalue problems for nonlinear elliptic operators abstract this paper solves the following form of normalized eigenvalue problem a u c u 0 0 and u d where d is a bounded open set in a real infinite dimensional banach space x and both x and its dual x are locally uniformly convex a is an unbounded maximal monotone operator on x the operators c is defined and continuous only on r d such that zero is not in the weak closure of a subset of c u c u this research reveals the fact that such eigenvalue problems do not depend on any properties of c located in r d this remarkable discovery extends theorem 4 in a g kartsatos i v skrypnik normalized eigenvalues for nonlinear abstract and elliptic operators j differential equations 155 1999 443 475 and is applied to the nonlinear elliptic operators under degenerate and singular conditions

partial differential equations involving subcritical critical and supercritical nonlinearities abstract we establish the existence of at least one nonnegative solution for the problem p div a u u f u in u 0 on where a and f satisfy conditions near zero here the novelty is that we do not need restrictions on the nonlinearities at infinity therefore we can consider subcritical critical and supercritical cases

numerical analysis of a frictionless viscoelastic contact problem with normal damped response abstract we consider a mathematical model which describes the frictionless contact between a viscoelastic body and a deformable foundation we model the material s behavior with a nonlinear kelvin voigt constitutive law the process is assumed to be quasistatic and the contact is modeled with a general normal damped response condition we present the variational formulation of the problem including the existence of a unique weak solution to the model we then study the numerical approach to the problem using a fully discrete finite elements scheme with an explicit discretization in time we state the existence of the unique solution for the scheme and derive an error estimate on the approximate solutions finally we present some numerical results involving examples in one and two dimensions