periodic impact behavior of a class of hamiltonian oscillators with obstacles abstract in this paper we study the existence of harmonic and subharmonic solutions of a class of non smooth hamiltonian systems then apply its results to the vibration problems x q x x 2 g t x f t x t 0 x t 0 x t 0 if x t 0 0 infinitely many harmonic and subharmonic bouncing solutions are always obtained if q x satisfies some coercive conditions

nonlinear eigenvalue neumann problems with discontinuities in this paper we study nonlinear eigenvalue problems with neumann boundary conditions and discontinuous terms first we consider a nonlinear problem involving the p laplacian and we prove the existence of a solution for the multivalued approximation of it then we pass to semilinear problems and we prove the existence of multiple solutions the approach is based on the critical point theory for nonsmooth locally lipschitz functionals

some existence results for a periodic problem with non smooth potential abstract in this paper two existence results for a class of second order periodic boundary value problems with non smooth potential are obtained we extend the castro lazer thews reduction method to non smooth functionals the obtained result is then exploited to prove the existence of a nontrivial solution furthermore we prove the existence of multiple solutions by using a multiplicity result based on local linking

multivalued elliptic equation with exponential critical growth in r2 abstract in this work we study the existence of nontrivial solutions for the following class of multivalued elliptic problems p u v x u h x t f x u in r 2 where 0 v is a continuous function verifying some conditions h h 1 r 2 and t f x u is the generalized gradient of f x t with respect to t and f x t 0 t f x s d s assuming that f is a discontinuous function with exponential critical growth we have applied variational methods for locally lipschitz functional to get two solutions for p when is small enough

existence and multiplicity of solutions for a discontinuous problems with critical sobolev exponents abstract in this paper we consider the equation p u u p 2 u f x u in r n with discontinuous nonlinearity where 1 p n 0 is a real parameter and p n p n p is the critical sobolev exponent under proper conditions on f applying the nonsmooth critical point theory for locally lipschitz functionals we obtain at least one nontrivial nonnegative solution provided that 0 and for any k n it has k pairs of nontrivial solutions if k where 0 and k are positive numbers in particular we obtain the existence results for f is discontinuous in just one point

xpath satisfiability in the presence of dtds we study the satisfiability problem associated with xpath in the presence of dtds this is the problem of determining given a query p in an xpath fragment and a dtd d whether or not there exists an xml document t such that t conforms to d and the answer of p on t is nonempty we consider a variety of xpath fragments widely used in practice and investigate the impact of different xpath operators on the satisfiability analysis we first study the problem for negation free xpath fragments with and without upward axes recursion and data value joins identifying which factors lead to tractability and which to np completeness we then turn to fragments with negation but without data values establishing lower and upper bounds in the absence and in the presence of upward modalities and recursion we show that with negation the complexity ranges from pspace to exptime moreover when both data values and negation are in place we find that the complexity ranges from nexptime to undecidable furthermore we give a finer analysis of the problem for particular classes of dtds exploring the impact of various dtd constructs identifying tractable cases as well as providing the complexity in the query size alone finally we investigate the problem for xpath fragments with sibling axes exploring the impact of horizontal modalities on the satisfiability analysis

ordered and unordered tree inclusion the following tree matching problem is considered given labeled trees p and t can p be obtained from t by deleting nodes deleting a node u entails removing all edges incident to u and if u has a parent v replacing the edge from v to u by edges from v to the children of u the problem is motivated by the study of query languages for structured text databases simple solutions to this problem require exponential time for ordered trees an algorithm is presented that requires o p t time and space the corresponding problem for unordered trees is also considered and a proof of its np completeness is given an algorithm is presented for the unordered problem this algorithm works in o p t time if the out degrees of the nodes in p are bounded by a constant and in polynomial time if they are o log t

the monotone iterative technique for a parabolic boundary value problem with discontinuous nonlinearity let be a bounded lebesgue measurable domain of r n with a lipschitz boundary the following initial boundary value problem is considered u t lu f u h in q bu o on u 0 where q o t o t and 0 0 l is a uniformly elliptic operator b a boundary operator defined by bu u v bu in which v denotes the outer normal derivative on and f represents a discontinuous non linearity

critical point theory for nonsmooth functionals abstract in this paper we develop critical point theory for nonsmooth functional f h 0 1 r defined by f u 1 2 i j 1 a i j x u d i u d j u d x g x u d x the corresponding deformation lemmas are proved with the application to the bifurcation for quasilinear schrodinger equations in mind we extend the obtained results to that for a functional defined on a product space and prove a generalized saddle point theorem

infinitely many solutions for a differential inclusion problem in r n abstract in this paper we consider the differential inclusion problem di p u u p 2 u x f u x x r n u w 1 p r n where 2 n p l 1 r n l r n is radially symmetric and f stands for the generalized gradient of a locally lipschitz function f r r under suitable oscillatory assumptions on the potential f at zero or at infinity we show the existence of infinitely many radially symmetric solutions of di no symmetry requirement on f is needed our approach is based on a non smooth ricceri type variational principle developed by marano and motreanu j differential equations 182 2002 108 120

existence results for obstacle problems for nonlinear hemivariational inequality at resonance in this paper we are interested in studying the existence of solutions to obstacle problems for nonlinear hemivariational inequality at resonance driven by the p laplacian using a variational approach based on the nonsmooth critical point theory for nondifferentiable functionals we prove two existence theorems

on a class of damped vibration problems with obstacles and without direct variational structures the main purpose of this paper is to study the following damped vibration problems x q x x 2 f t with x 0 x 2 x 0 x 2 0 x t 0 t r and x t0 x t0 if x t0 0 where x t0 limt t0 0x t and x t0 limt t0 0x t the variational sets are given and some multiplicity results of periodic solutions satisfying the presented equations are obtained

nonlinear hemivariational inequalities at resonance in this paper we examine a semilinear hemivariational inequality at resonance in the first eigenvalue 1 of h01 z we prove two existence theorems for such problems our approach is variational and is based on the nonsmooth critical point theory of chang which uses the subdifferential calculus of clarke for locally lipschitz functions

critical points for nondifferentiable functions in presence of splitting a classical critical point theorem in presence of splitting established by brezis nirenberg is extended to functionals which are the sum of a locally lipschitz continuous term and of a convex proper lower semicontinuous function the obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational hemivariational eigenvalue problems

structural properties of xpath fragments we study structural properties of each of the main sublanguages of navigational xpath w3c recommendation commonly used in practice first we characterize the expressive power of these language fragments in terms of both logics and tree patterns second we investigate closure properties focusing on the ability to perform basic boolean operations while remaining within the fragment we give a complete picture of the closure properties of these fragments treating xpath expressions both as functions of arbitrary nodes in a document tree and as functions that are applied only at the root of the tree finally we provide sound and complete axiom systems and normal forms for several of these fragments these results are useful for simplification of xpath expressions and optimization of xml queries

on a new notion of linking and application to elliptic problems at resonance abstract in this paper we introduce a new notion of linking which includes in particular the notions of homotopical linking and local linking critical point theorems for continuous functionals on metric spaces are presented finally an application to nonlinear elliptic problems at resonance is given

infinitely many solutions for a neumann type differential inclusion problem involving the p x laplacian abstract in this paper we consider a differential inclusion problem involving the p x laplacian of the type div u p x 2 u x u p x 2 u f x u g x u in u 0 on we prove the existence of infinitely many solutions of this problem under suitable hypotheses by applying a non smooth ricceri type variational principle and the theory of the variable exponent sobolev spaces

on a class of forced vibration problems with obstacles abstract the main purpose of this paper is to study the following damped vibration problems 1 1 x q x x 2 g t x f t with 1 2 x 0 x 2 x 0 x 2 0 x t 0 t r and 1 3 x t 0 x t 0 if x t 0 0 where x t 0 lim t t 0 0 x t x t 0 lim t t 0 0 x t the variational sets are given and some multiplicity results of periodic solutions satisfying 1 1 1 2 1 3 are obtained

elliptic problems with lack of compactness via a new fixed point theorem abstract this paper provides a new fixed point theorem for increasing self mappings g b b of a closed ball b x where x is a banach semilattice which is reflexive or has a weakly fully regular order cone x by means of this fixed point theorem we are able to establish existence results of elliptic problems with lack of compactness

an existence result for gradient type systems with a nondifferentiable term on unbounded strips in this paper we study the existence of nontrivial solutions for a class of gradient type systems on strip like domains where the nonlinear term is not necessarily continuously differentiable the proof of the main result is based on a nonsmooth version of the mountain pass theorem which involves the cerami compactness condition and on the principle of symmetric criticality for locally lipschitz functions

closed geodesics with lipschitz obstacle abstract geodesics on a general subsetmof r nare considered whenmis the closure of an open subset with lipschitz boundary and suitable topological conditions are fulfilled the existence of a nonconstant closed geodesic is proved

existence and multiplicity of solutions for a class of forced vibration problems with obstacles abstract by variational methods an existence theorem and two multiplicity theorems of solutions of the following forced vibration problems are obtained 1 1 x q x x 2 g t x f t with 1 2 x 0 x 2 x 0 x 2 0 x t 0 t r and 1 3 x t 0 x t 0 if x t 0 0 where x t 0 lim t t 0 0 x t x t 0 lim t t 0 0 x t

existence of solutions for hyperbolic hemivariational inequalities in this paper we study a hyperbolic hemivariational inequality with a nonlinear pseudomonotone operator depending on the derivative of an unknown function and a linear monotone operator depending on an unknown function using the surjectivity result for l pseudomonotone operators an existence result for such inequalities is proved

multiple solutions for nonlinear elliptic equations at resonance with a nonsmooth potential abstract in this paper we study a nonlinear elliptic problem at resonance driven by the p laplacian and with a nonsmooth potential hemivariational inequality our approach is variational and it is based on the nonsmooth critical point theory for locally lipschitz functions due to chang we prove a theorem guaranteeing the existence of one solution which is smooth and strictly positive then by strengthening the assumptions we establish a multiplicity result providing the existence of at least two distinct solutions our hypotheses permit resonance and asymmetric behavior at and as a byproduct of our analysis we obtain an nonlinear and nonsmooth generalization of a result of brezis nirenberg about h 0 1 versus c 0 1 minimizers of a smooth functional

solutions and multiple solutions for periodic systems with nonhomogeneous differential operators abstract in this paper we consider nonlinear periodic systems driven by the nonhomogeneous vector p laplacian differential operator and with a nonsmooth potential using variational techniques based on the nonsmooth critical point theory we prove existence and multiplicity results finally we obtain an existence result for systems driven by the ordinary vector p laplacian and we show that it is still true in the more general framework of the previous results

on the existence of small energy solutions for a sublinear neumann problem abstract in this paper we are concerned with the sublinear problem 0 1 u u p 2 u in u 0 on where r n is a bounded domain and 1 p 2 for p 1 the nonlinearity u p 2 u will be identified by sgn u in contrast to previous work on the dirichlet problem some difficulties arise due to the fact that the associated energy functional is not bounded from below complementing recent work by parini and weth in 15 on least energy solutions we prove that 0 1 has infinitely many solutions with small negative energy

subharmonic solutions of sublinear second order systems with impacts abstract we mainly consider subharmonic bouncing solutions of sublinear second order systems with an obstacle based on variational method

on a class of semilinear schrodinger equations involving critical growth and discontinuous nonlinearities abstract in this paper we deal with a class of schrodinger equation in r n involving critical sobolev exponent and jump discontinuities the basic tool employed here is an approximation technique with periodic functions and variational arguments based on a linking theorem for locally lipschitz functionals

existence of solutions for elliptic hemivariational inequalities abstract this paper is devoted to the existence of solutions concerning the dirichlet problem for quasilinear elliptic hemivariational inequalities at the first eigenvalue using the notion of the generalized gradient of clarke and the property of the first eigenfunction some existence results of solutions have been proved

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

local c1 ω minimizers versus local w1 p ω minimizers of nonsmooth functionals abstract we study not necessarily differentiable functionals of the form j u 1 p u p d x 1 p u p d x j 1 x u d x j 2 x u d with 1 p involving locally lipschitz functions j 1 r r as well as j 2 r r we prove that local c 1 minimizers of j must be local w 1 p minimizers of j

dynamic contact problem for viscoelastic piezoelectric materials with normal damped response and friction in this paper we deal with a class of inequality problems for dynamic frictional contact between a piezoelectric body and a foundation the model consists of a system of the hemivariational inequality of hyperbolic type for the displacement the time dependent elliptic equation for the electric potential the contact is modeled by a general normal damped response condition and a friction law which are nonmonotone possibly multivalued and have the subdifferential form the existence of a weak solution to the model is proved by embedding the problem into a class of second order evolution inclusions and by applying a surjectivity result for multivalued operators

dirichlet problem with discontinuous nonlinearities super linear or asymptotically linear at infinity in the present paper a class of dirichlet problem with discontinuous nonlinearities super linear or asymptotically linear at infinity is studied and some new existence theorems of solutions are obtained

entire solutions of multivalued nonlinear schrodinger equations in sobolev spaces with variable exponent abstract we establish the existence of an entire solution for a class of stationary schrodinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows up at infinity the abstract framework is related to lebesgue sobolev spaces with variable exponent the proof is based on the critical point theory in the sense of clarke and we apply chang s version of the mountain pass lemma without the palais smale condition for locally lipschitz functionals our result generalizes in a nonsmooth framework a result of rabinowitz p h rabinowitz on a class of nonlinear schrodinger equations z angew math phys zamp 43 1992 270 291 on the existence of ground state solutions of the nonlinear schrodinger equation

on the eigenvalue problem for hemivariational inequalities existence and multiplicity of solutions in this article the eigenvalue problem for hemivariational inequalities is studied first some existence results are obtained by applying a critical point method suitable for nonconvex nonsmooth energy functions further some results concerning the multiplicity of solutions are proved applications from mechanics illustrate the theory

on existence of solutions for parabolic hemivariational inequalities abstract a class of parabolic hemivariational inequalities is considered in which the energy function is locally lipschitz not necessarily convex or differentiable and the nonlinear evolution operator is multivalued and generalized pseudomonotone using techniques of multivalued analysis and a surjectivity result for l generalized pseudomonotone operators we prove the existence for a cauchy problem and a periodic problem some applications to nonsmooth mechanics are also indicated

existence of solutions for wave type hemivariational inequalities with noncoercive viscosity damping abstract in this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form u au bu j u f where b is a linear elliptic operator and a is linear and nonnegative not necessarily coercive

existence of positive and of multiple solutions for nonlinear periodic problems abstract in this paper we consider a scalar periodic problem driven by the ordinary p laplacian differential operator and having a nonsmooth potential using a variational method based on nonsmooth critical point theory first we prove the existence of a strictly positive solution then by strengthening our hypotheses on the nonsmooth potential we prove the existence of a second periodic solution

periodic problems with asymmetric nonlinearities and nonsmooth potentials abstract we consider a nonlinear periodic boundary value problem driven by the ordinary scalar p laplacian and with a nonsmooth locally lipschitz potential which exhibits an asymmetric behaviour at and at using the fucik spectrum and a variational approach based on the nonsmooth critical point theory we obtain a solution for the problem using a general minimax principle concerning linking sets

multiple solution results for elliptic neumann problems involving set valued nonlinearities abstract the main goal of this paper is to present multiple solution results for elliptic inclusions of clarke s gradient type under nonlinear neumann boundary conditions involving the p laplacian and set valued nonlinearities to be more precise we study the inclusion p u f x u u p 2 u in with the boundary condition u p 2 u a u p 1 b u p 1 g x u on we prove the existence of two constant sign solutions and one sign changing solution depending on the parameters a and b our approach is based on truncation techniques and comparison principles for elliptic inclusions along with variational tools like the nonsmooth mountain pass theorem the second deformation lemma for locally lipschitz functionals as well as comparison results of local c 1 minimizers and local w 1 p minimizers of nonsmooth functionals

on some elliptic hemivariational and variational hemivaritional inequalities abstract the existence of solutions to an elliptic hemivariational inequality involving the p laplacian is first established the variational hemivariational case which includes the above one is then examined when p 2 both of them are chiefly treated through mountain pass like critical point results for non differentiable functions

fast homoclinic solutions for a class of damped vibration problems in this paper we deal with the existence and multiplicity of homoclinic solutions of the following damped vibration problemsu t q t u t l t u t w t u t 0 where l t and w t x are neither autonomous nor periodic in t our approach is variational and it is based on the critical point theory we prove existence and multiplicity results of fast homoclinic solutions under general growth conditions on the potential function moreover some open problems proposed by zhang and ruan are resolved our theorems appear to be the first such result

nonlinear algebraic systems with discontinuous terms abstract using a multiple critical points theorem for locally lipschitz continuous functionals we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and positive definite matrix applications to tridiagonal fourth order and partial difference inclusions are presented

volume growth temperedness and integrability of matrix coefficients on a real spherical space abstract we apply the local structure theorem from 13 and the polar decomposition of 12 to a real spherical space z g h and control the volume growth on z we define the harish chandra schwartz space on z we give a geometric criterion to ensure l p integrability of matrix coefficients on z

a new critical point theorem for locally lipschitz functionals with applications to differential equations abstract in the present paper a new critical point theorem for locally lipschitz functions is given and as applications one existence and two multiplicity results for zero boundary value problems are obtained several important classical theorems are improved

a variational approach to discontinuous problems with critical sobolev exponents abstract we employ variational techniques to study the existence and multiplicity of positive solutions of semilinear equations of the form u h x h u a uq u2 1 in rn where a 0 are parameters h x is both nonnegative and integrable on rn h is the heaviside function 2 is the critical sobolev exponent and 0 q

hemivariational inequalities for stationary navier stokes equations in this paper we study a class of inequality problems for the stationary navier stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain the equations are nonlinear navier stokes ones for the velocity and pressure with nonstandard boundary conditions we assume the nonslip boundary condition together with a clarke subdifferential relation between the pressure and the normal components of the velocity the existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps we also establish a result on the dependence of the solution set with respect to a locally lipschitz superpotential appearing in the boundary condition

differential inclusions involving oscillatory terms abstract motivated by mechanical problems where external forces are non smooth we consider the differential inclusion problem d u x f u x g u x in u 0 in u 0 on where r n is a bounded open domain and f and g stand for the generalized gradients of the locally lipschitz functions f and g in this paper we provide a quite complete picture on the number of solutions of d whenever f oscillates near the origin infinity and g is a generic perturbation of order p 0 at the origin infinity respectively our results extend in several aspects those of kristaly and morosanu 2010

uniform convexity of musielak orlicz sobolev spaces and applications abstract this paper deals with uniform convexity of musielak orlicz sobolev spaces and its applications to variational problems some sufficient conditions and examples for uniform convexity of musielak orlicz sobolev spaces are given some special properties relative to the uniformly convex modular for uniformly convex musielak orlicz sobolev spaces are presented as an application of these abstract results the local minimizers and the mountain pass type critical point of an integral functional with more complicated growth than the p x growth are studied

nonsmooth critical point theory on closed convex sets and nonlinear hemivariational inequalities abstract in this paper we develop a critical point theory for nonsmooth locally lipschitz functionals defined on a closed convex set extending this way the work of struwe variational methods springer berlin 1990 through a deformation result we obtain minimax principles producing critical points then we use the theory to obtain positive and negative solutions of nonlinear and semilinear hemivariational inequalities in this context we improve a result on positive solutions for semilinear elliptic problems due to nirenberg variational methods in nonlinear problems in topics in calculus of variations lecture notes in mathematics vol 1365 springer berlin 1987

boundary value problems for discontinuous perturbations of singular ϕ laplacian operator abstract systems of differential inclusions of the form u f t u t 0 t where with strictly convex is a homeomorphism of the ball b a r n onto r n are considered under dirichlet periodic and neumann boundary conditions here f t x stands for the generalized clarke gradient of f t at x r n using nonsmooth critical point theory we obtain existence results under some appropriate conditions on the potential f examples of applications concerning filippov type solutions are also provided

nonsmooth version of fountain theorem and its application to a dirichlet type differential inclusion problem abstract in this paper we establish a nonsmooth version of fountain theorem by adopting the framework of nonsmooth analysis theory which is a generalization of theorem 3 6 of willem 1996 2 then we present an application of this theorem to a dirichlet type differential inclusion problem

existence and multiplicity results for some elliptic systems with discontinuous nonlinearities abstract in this paper we complete two tasks we first extend the critical point theorem obtained by li and willem s j li m willem applications of local linking to critical point theory j math anal appl 189 1995 6 32 to the nonsmooth case in which the energy functional is locally lipschitz and satisfies the weaker nonsmooth cerami condition then we study some semilinear elliptic systems with discontinuous nonlinearities and obtain some existence and multiplicity results

transitive closure logic nested tree walking automata and xpath we study fo mtc first order logic with monadic transitive closure a logical formalism in between fo and mso on trees we characterize the expressive power of fo mtc in terms of nested tree walking automata using the latter we show that fo mtc is strictly less expressive than mso solving an open problem we also present a temporal logic on trees that is expressively complete for fo mtc in the form of an extension of the xml document navigation language xpath with two operators the kleene star for taking the transitive closure of path expressions and a subtree relativisation operator allowing one to restrict attention to a specific subtree while evaluating a subexpression we show that the expressive power of this xpath dialect equals that of fo mtc for boolean unary and binary queries we also investigate the complexity of the automata model as well as the xpath dialect we show that query evaluation be done in polynomial time combined complexity but that emptiness or satisfiability is 2exptime complete

the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation the dual variational principle and equilibria for a beam resting on a discontinuous nonlinear elastic foundation m r grossinho a b 1 st a tersian c 2 a departamento de matem atica iseg universidade t ecnica de lisboa rua do quelhas 6 1200 lisboa portugal b cmaf universidade de lisboa av prof gama pinto 2 1699 lisboa codex portugal c center of applied mathematics and informatics university of rousse 8 studentska str 7017 rousse bulgaria

three solutions for a neumann type differential inclusion problem involving the p x laplacian abstract in this paper we consider neumann type differential inclusion problems involving the p x laplacian of the type div u p x 2 u u p x 2 u f x u in u 0 on applying a version of the non smooth three critical points theorem we obtain the existence of three solutions of the problem in w 0 1 p x

surjection and inversion for locally lipschitz maps between banach spaces abstract we study the global invertibility of non smooth locally lipschitz maps between infinite dimensional banach spaces using a kind of palais smale condition to this end we consider the chang version of the weighted palais smale condition for locally lipschitz functionals in terms of the clarke subdifferential as well as the notion of pseudo jacobians in the infinite dimensional setting which are the analog of the pseudo jacobian matrices defined by jeyakumar and luc using these tools we obtain the existence and uniqueness of solution for certain nonlinear equations defined by locally lipschitz mappings along the way we also obtain a global surjection theorem for locally lipschitz maps in terms of pseudo jacobians

functional regularity properties for light rays in general relativity in this note we consider some functionals restricted to the nonholonomic constraint satisfied by lightlike curves in lorentzian manifolds these functionals are related to the arrival time map whose critical points are light rays in general relativity and they have been used in the variational theory of light rays in some recent literatures we exhibit an explicit example showing that from a functional point of view the constraint above does not have sufficient regularity nevertheless we show that up to a continuous change in coordinates the used functionals restricted to the constraint have just the regularity that one needs to develop lusternik schnirelmann theory or morse theory

invariant tori in hamiltonian systems with impacts it is shown that a large class of solutions in two degree of freedom hamiltonian systems of billiard type can be described by slowly varying one degree of freedom hamiltonian systems under some non degeneracy conditions such systems are found to possess a large set of quasiperiodic solutions filling out two dimensional tori which correspond to caustics in the classical billiard this provides a unified proof of existence of quasiperiodic solutions in convex billiards and other systems with impacts including classical billiard in electric and magnetic fields dual billiard and fermi ulam systems