correlation functions for random complex zeroes strong clustering and local universality we prove strong clustering of k point correlation functions of zeroes of gaussian entire functions in the course of the proof we also obtain universal local bounds for k point functions of zeroes of arbitrary nondegenerate gaussian analytic functions in the second part of the paper we show that strong clustering yields the asymptotic normality of fluctuations of some linear statistics of zeroes of gaussian entire functions in particular of the number of zeroes in measurable domains of large area this complements our recent results from the paper fluctuations in random complex zeroes

infinitely many non negative solutions for a dirichlet problem involving p x laplacian abstract in this paper we consider a dirichlet problem involving the p x laplacian of the type div u p x 2 u f x u in u 0 on we prove the existence of infinitely many non negative solutions of the problem by applying a general variational principle due to b ricceri and the theory of the variable exponent sobolev spaces

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

dynamic lagrangian computations for solids with variable nodal connectivity for severe distortions this paper presents an algorithm for dynamic lagrangian computations for solids in plane strain geometry with variable nodal connectivity to allow for severe distortions the nodes are somewhat analogous to flexible circular disks when they move closer together than their equilibrium distance they generate compressive repulsive forces conversely when they move apart they generate tensile attractive forces material strength effects are also included because a node can only be affected by its neighbour nodes the approach has been designated the nabor approach the key to this approach is that it is possible to have variable nodal connectivity a node can acquire new neighbours thus allowing all forms of distortion the nabor algorithm has been incorporated as an option into the explicit finite element code epic 2 by using both the nabor grid and the epic 2 finite element grid together it is possible to perform lagrangian computations for a wide range of problems

existence of infinitely many solutions for a neumann problem involving the p x laplacian abstract in this paper we consider the neumann 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 the problem under weaker hypotheses by applying a variational principle due to b ricceri and the theory of the variable exponent sobolev spaces our results are an improvement and generalization of the relative results obtained by b ricceri for the p laplacian case

detection of arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms we propose a direct approach for detecting arbitrarily many solutions for perturbed elliptic problems involving oscillatory terms although the method works in various frameworks we illustrate it on the problem

a variational approach to multiplicity results for boundary value problems on the real line we study the existence and multiplicity of solutions for a parametric equation driven by the p laplacian operator on unbounded intervals precisely by using a recent local minimum theorem we prove the existence of a non trivial non negative solution to an equation on the real line without assuming any asymptotic condition either at 0 or at on the nonlinear term as a special case we note the existence of a non trivial solution for the problem when the nonlinear term is sublinear at 0 moreover under a suitable superlinear growth at on the nonlinearity we prove a multiplicity result for such a problem

variational structure and multiple solutions for a fractional advection dispersion equation by establishing a variational structure and using the critical point theory we investigate the existence of multiple solutions for a class of fractional advection dispersion equations arising from a symmetric transition of the mass flux several criteria for the existence of multiple nonzero solutions are established under certain assumptions

a critical point theorem and existence results for a nonlinear boundary value problem in this paper the existence of non zero solutions to a neumann boundary value problem is established multiplicity results are also pointed out the approach is based on a novel critical point theorem

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

a brezis nirenberg splitting approach for nonlocal fractional equations in this paper we consider problems modeled by the following nonlocal fractional equation su a x u f u in u 0in rn where s 0 1 is fixed is an open bounded subset of rn n 2s with lipschitz boundary s is the fractional laplace operator and is a real parameter under two different types of conditions on the functions a and f by using a famous critical point theorem in the presence of splitting established by brezis and nirenberg we obtain the existence of at least two nontrivial weak solutions for our problem

existence and multiplicity of solutions for a neumann problem involving the p x laplace operator abstract in this paper we study the following nonlinear neumann boundary value problem div u p x 2 u u p x 2 u f x u x t r u v 0 x t r where r n is a bounded domain with smooth boundary u v is the outer unit normal derivative on 0 is a real number p is a continuous function on with inf x p x 1 f r r is a continuous function using the three critical point theorem due to ricceri under the appropriate assumptions on f we establish the existence of at least three solutions of this problem some known results are generalized

infinitely many solutions for a class of discrete non linear boundary value problems the existence of infinitely many solutions for a discrete non linear dirichlet problem involving the p laplacian under appropriate oscillating behaviours of the non linear term is established the approach is based on the critical point theory

multiplicity results for a neumann problem involving the p laplacian abstract in this paper we establish some multiplicity results for the following neumann problem div u p 2 u x u p 2 u x f u in u 0 on the multiple solutions are obtained by combining an existence theorem recently proved by g anello and g cordaro with well known critical point theorems

existence of infinitely many weak solutions for a neumann problem abstract the aim of this paper is to establish a critical point theorem for functionals defined on a reflexive real banach space via a variational principle of ricceri as a consequence an existence theorem of infinitely many weak solutions for a neumann problem involving the p laplacian with p 1 is obtained

perturbed kirchhoff type neumann problems in orlicz sobolev spaces the aim of this paper is to establish the existence of infinitely many solutions for perturbed kirchhoff type non homogeneous neumann problems involving two parameters to be precise we prove that an appropriate oscillating behaviour of the nonlinear term even under small perturbations ensures the existence of infinitely many solutions our approach is based on recent variational methods for smooth functionals defined on orlicz sobolev spaces

remarks on ricceri s variational principle and applications to the p x laplacian equations abstract in this paper we give some remarks on a variational principle of ricceri in the case of sequentially weakly lower semi continuous functionals defined on a reflexive real banach space in particular we introduce the notions of ricceri block and ricceri box which are more convenient in some applications than the weakly connected components using the variational principle of ricceri and a local mountain pass lemma we study the multiplicity of solutions of the p x laplacian equations with neumann dirichlet or no flux boundary condition and under appropriate hypotheses in which the integral functionals need not satisfy the ps condition on the global space we prove that the problem has at least seven solutions

quasilinear elliptic non homogeneous dirichlet problems through orlicz sobolev spaces abstract in this paper we are interested in the existence of infinitely many weak solutions for a non homogeneous eigenvalue dirichlet problem by using variational methods in an appropriate orlicz sobolev setting we determine intervals of parameters such that our problem admits either a sequence of non negative weak solutions strongly converging to zero provided that the non linearity has a suitable behaviour at zero or an unbounded sequence of non negative weak solutions if a similar behaviour occurs at infinity

minimization on spheres of coercive functionals on w01 2 ω abstract we deal with the minimization on spheres of functionals defined on the space w 0 1 2 we apply the main results to establish a multiplicity theorem for a dirichlet problem involving equations of the type u h x u s 2 u g x u here is the laplacian operator is a real parameter s 1 2 h c is a function which is allowed to be sign changing and g r r r n is a caratheodory function having no growth conditions with respect to the second variable

a compact embedding result for anisotropic sobolev spaces associated to a strip like domain and some applications abstract let m 1 and d 2 be integers and consider a strip like domain o r d where o r m is a bounded euclidean domain with smooth boundary furthermore let p o r d r be a uniformly continuous and cylindrically symmetric function we prove that the subspace of w 1 p x y o r d consisting of the cylindrically symmetric functions is compactly embedded into l o r d provided that m d p inf x y o r d p x y p sup x y o r d p x y as an application we study a neumann problem involving the p x y laplacian operator and an oscillating nonlinearity proving the existence of infinitely many cylindrically symmetric weak solutions our approach is based on variational and topological methods in addition to the principle of symmetric criticality

multiplicity of nontrivial solutions for quasilinear elliptic equation two nontrivial solutions are obtained by the reduction method for the nonautonomous semilinear elliptic dirichlet boundary value problem some well known multiplicity results are generalized

on the nonlinear schrodinger equation on the poincare ball model abstract in this paper we prove the existence of a sequence of nonnegative weak solutions for the following problem h u u f u in b n u h 1 2 b n where h denotes the laplace beltrami operator on the poincare ball model b n with n 3 of the hyperbolic space h n l 1 b n l b n is a nonnegative and not identically zero radially symmetric potential f is a suitable continuous function and is a positive real parameter the analysis developed in this paper combines a compactness embedding result due to skrzypczak and tintarev 2013 theorem 1 3 and proposition 3 1 some group theoretical arguments on the poincare ball model b n and variational methods for smooth functionals defined on the sobolev space h 1 2 b n associated to the homogeneous hadamard manifold b n

infinitely many solutions for a dirichlet problem involving the p laplacian the existence of infinitely many solutions for an autonomous elliptic dirichlet problem involving the p laplacian is investigated the approach is based on variational methods

on normal approximations of distributions in terms of dependency graphs l auteur interprete les bornes de l erreur introduites par stein dans l approximation normale de sommes de variables aleatoires dependantes en termes de graphes de dependance ceci mene a des ameliorations d un theoreme de limite centrale de petrovskaya et leontovich et de recentes applications de baldi et rinatt en particulier on obtient des bornes pour des taux de convergence on etudie ensuite l approximation normale du nombre de maximums locaux d une fonction aleatoire sur un graphe

existence results for fractional differential systems through a local minimization principle in this paper we investigate the existence of one weak solution for a class of fractional differential systems the approach is based on variational methods for smooth functionals defined on reflexive banach spaces the main result is also demonstrated with examples

multiple critical points theorems without the palais smale condition abstract in this paper multiple critical points theorems where the palais smale condition on the functional is not requested are presented as an application multiple solutions for a quasilinear two point boundary value problem involving the one dimensional p laplacian are obtained

infinitely many solutions to elliptic problems with variable exponent and nonhomogeneous neumann conditions abstract the aim of this paper is to establish the existence of an unbounded sequence of weak solutions for a class of differential equations with p x laplacian and subject to small perturbations of nonhomogeneous neumann conditions the approach is based on variational methods

infinitely many positive solutions for kirchhoff type problems abstract this paper is concerned with the existence of infinitely many positive solutions to a class of kirchhoff type problem a b u 2 d x u f x u in and u 0 on where is a smooth bounded domain of r n a b 0 0 and f r r is a caratheodory function satisfying some further conditions we obtain a sequence of a e positive weak solutions to the above problem tending to zero in l with f being more general than that of k perera z zhang nontrivial solutions of kirchhoff type problems via the yang index j differential equations 221 2006 246 255 z zhang k perera sign changing solutions of kirchhoff type problems via invariant sets of descent flow j math anal appl 317 2006 456 463

existence and multiplicity of solutions for a class of semilinear elliptic equations the existence and multiplicity results are obtained for solutions of a class of the dirichlet problem for semilinear elliptic equations by the least action principle and the minimax methods respectively

a neumann boundary value problem for the sturm liouville equation abstract in this paper we prove the existence of infinitely many solutions to a neumann boundary value problem for the sturm liouville equation results of the existence of three solutions are also established the approach is based on multiple critical points theorems

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

arbitrarily many solutions for a perturbed p x laplacian equation involving oscillatory terms this paper deals with a perturbed p x laplacian equation involving oscillatory terms div u p x email protected u u p x 2u q x f u email protected u email protected r n u 0 u x 0as x by using variational methods and the non smooth version symmetric criticality principle we establish a the unperturbed problem p 0 has infinitely many distinct solutions b the number of distinct solutions for p e becomes greater and greater whenever e is smaller and smaller our results are a generalization of the case of laplacian from kristaly to the case of p x laplacian

perturbation for a p x laplacian equation involving oscillating nonlinearities in rn abstract in this paper we study multiple solutions of the following problem in r n 0 1 div u p x 2 u u p x 2 u f x u g x u u w 1 p x r n where the potential f x t 0 t f x s d s has a suitable oscillating behavior in any neighborhood of the origin respectively and g is a perturbation term our results are a generalization of the case of the constant exponent and bounded domain from g anello g cordaro perturbation from dirichlet problem involving oscillating nonlinearities j differential equations 234 2007 80 90 to the case of variable exponent and r n

existence and multiplicity of solutions for fourth order boundary value problems with parameters abstract in this paper we study the existence and multiplicity of the solutions for the fourth order boundary value problem bvp u 4 t u t u t f t u t 0 t 1 u 0 u 1 u 0 u 1 0 where f 0 1 r r is continuous r and r are parameters by means of the idea of the decomposition of operators shown by chen w y chen a decomposition problem for operators xuebao of dongbei renmin university 1 1957 95 98 see also m krasnosel skii topological methods in the theory of nonlinear integral equations gostehizdat moscow 1956 and the critical point theory we obtain that if the pair is on the curve 2 4 satisfying 2 2 then the above bvp has at least one two three and infinitely many solutions for being in different interval respectively

elliptic problems on complete non compact riemannian manifolds with asymptotically non negative ricci curvature abstract in this paper we discuss the existence and non existence of weak solutions to parametric equations involving the laplace beltrami operator g in a complete non compact d dimensional d 3 riemannian manifold m g with asymptotically non negative ricci curvature and intrinsic metric d g namely our simple model is the following problem g w v w f w in m w 0 in m where v is a positive coercive potential is a positive bounded function is a real parameter and f is a suitable continuous nonlinear term the existence of at least two non trivial bounded weak solutions is established for large value of the parameter requiring that the nonlinear term f is non trivial continuous superlinear at zero and sublinear at infinity our approach is based on variational methods no assumptions on the sectional curvature as well as symmetry theoretical arguments are requested in our approach

infinitely many solutions for a differential inclusion problem in rn involving the p x laplacian abstract in this paper we consider the differential inclusion problem in r n involving the p x laplacian of the type div u p x 2 u u p x 2 u f x u in r n u w 1 p x r n we prove the existence of infinitely many radially symmetric solutions of the problem under suitable hypotheses by applying a nonsmooth variational principle due to marano and motreanu and the theory of the variable exponent sobolev spaces

multiple constant sign and nodal solutions for nonlinear elliptic equations with the p laplacian we consider a nonlinear elliptic equation driven by the p laplacian with dirichlet boundary conditions using variational techniques combined with the method of upper lower solutions and suitable truncation arguments we establish the existence of at least five nontrivial solutions two positive two negative and a nodal sign changing solution our framework of analysis incorporates both coercive and p superlinear problems also the result on multiple constant sign solutions incorporates the case of concave convex nonlinearities

on nonlinear schrodinger equations on the hyperbolic space abstract we study existence of weak solutions for certain classes of nonlinear schrodinger equations on the poincare ball model b n n 3 by using the palais principle of symmetric criticality and suitable group theoretical arguments we establish the existence of a nontrivial weak solution

existence of three nontrivial solutions for nonlinear neumann hemivariational inequalities abstract in this paper we consider a nonlinear neumann problem driven by the p laplacian with a nonsmooth potential hemivariational inequality using minimax methods based on the nonsmooth critical point theory together with suitable truncation techniques we show that the problem has at least three nontrivial smooth solutions two of these solutions have constant sign one is positive the other negative

infinitely many periodic solutions for a second order nonautonomous system in this paper we are interested in multiplicity results for a second order nonautonomous system infinitely many solutions follow from a recent variational principle by b ricceri

on multiplicity of solutions of dirichlet problem for uniformly elliptic operator equations abstract in the present paper the following dirichlet problem a u f x u in u 0 on is studied and four new multiplicity results of solutions are obtained where r n is a bounded domain n 1 and a u i j 1 n d i a i j x d j u c x u a i j x a j i x c 1 i j 1 2 n c x c c x 0 and there is 0 such that i j 1 n a i j x i j 2 x r n

large deformation analysis of contact in degenerate shell elements a new formulation is presented for the analysis of contact in degenerate shell elements this formulation accounts for the transverse stress and strain through the shell thickness and can accommodate double sided shell contact the kinematic contact conditions are expressed accurately in terms of the physical shell contacting surfaces and the problem is formulated in terms of variational inequalities vi large deformations and rotations are accounted for by invoking the appropriate stress and strain measures the solution of the variational inequality is obtained using lagrange multipliers this guarantees that the kinematic contact constraints are accurately satisfied and that the solution is free from user defined parameters two examples involving three beams in contact and ring compression are simulated to establish the validity of the developed formulations and the solution technique 1998 john wiley sons ltd

existence of solutions for a perturbed dirichlet problem without growth conditions we present some results on the existence and multiplicity of solutions for boundary value problems involving equations of the type u f x u g x u where is the laplacian operator is a real parameter and f g r r rn are two caratheodory functions having no growth conditions with respect to the second variable the approach is variational and mainly based on a critical point theorem by b ricceri

central limit theorem for exponentially quasi local statistics of spin models on cayley graphs central limit theorems for linear statistics of lattice random fields including spin models are usually proven under suitable mixing conditions or quasi associativity many interesting examples of spin models do not satisfy mixing conditions and on the other hand it does not seem easy to show central limit theorem for local statistics via quasi associativity in this work we prove general central limit theorems for local statistics and exponentially quasi local statistics of spin models on discrete cayley graphs with polynomial growth further we supplement these results by proving similar central limit theorems for random fields on discrete cayley graphs taking values in a countable space but under the stronger assumptions of alpha mixing for local statistics and exponential alpha mixing for exponentially quasi local statistics all our central limit theorems assume a suitable variance lower bound like many others in the literature we illustrate our general central limit theorem with specific examples of lattice spin models and statistics arising in computational topology statistical physics and random networks examples of clustering spin models include quasi associated spin models with fast decaying covariances like the off critical ising model level sets of gaussian random fields with fast decaying covariances like the massive gaussian free field and determinantal point processes with fast decaying kernels examples of local statistics include intrinsic volumes face counts component counts of random cubical complexes while exponentially quasi local statistics include nearest neighbour distances in spin models and betti numbers of sub critical random cubical complexes

a critical point theorem via the ekeland variational principle abstract the aim of this paper is to establish the existence of a local minimum for a continuously g teaux differentiable function possibly unbounded from below without requiring any weak continuity assumption several special cases are also emphasized moreover a novel definition of palais smale condition which is more general than the usual one is presented and a mountain pass theorem is pointed out as a consequence multiple critical points theorems are then established finally as an example of applications an elliptic dirichlet problem with critical exponent is investigated

a general variational principle and some of its applications abstract in this paper given a reflexive real banach space x and two sequentially weakly lower semicontinuous functionals on x with strongly continuous and coercive we are mainly interested in the existence of infinitely many local minima of the functional for each sufficiently large r

infinitely many solutions for a perturbed nonlinear navier boundary value problem involving the p biharmonic abstract by using critical point theory we establish the existence of infinitely many weak solutions for a class of elliptic navier boundary value problems depending on two parameters and involving the p biharmonic operator

on the relationship between two three critical point theorems abstract in this paper we analyze the hypotheses of two theorems which have proven to be useful tools for obtaining the existence of three critical points in nonlinear problems in both cases the hypotheses can be stated in terms of some elementary inequalities involving coercive in a suitable sense sets of affine functions we prove that the two resulting inequalities are in fact equivalent

multiplicity results for perturbed fourth order kirchhoff type elliptic problems using variational methods and critical point theory we establish multiplicity results of nontrivial and nonnegative solutions for a perturbed fourth order kirchhoff type elliptic problem

on variational methods for a class of damped vibration problems abstract in the present paper the following damped vibration problems 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 and 1 1 u t q t u t a t u t f t u t a e t 0 t u 0 u t u 0 e q t u t 0 are studied where t 0 0 q l 1 0 t r q t 0 t q s d s a t a i j t is a symmetric n n matrix valued function defined in 0 t with a i j l 0 t for all i j 1 2 n and there exists a positive constant such that a t 2 for all r n and a e t 0 t the variational principles are given and an existence theorem and three multiplicity theorems of periodic solutions are obtained

multiple periodic solutions for second order systems with changing sign potential this paper deals with the multiplicity of solutions of a second order nonautonomous system we extend a previous result of the author relaxing the assumptions on the sign of the potential

infinitely many critical points of non differentiable functions and applications to a neumann type problem involving the p laplacian abstract for a family of functionals in a banach space which are possibly non smooth and depend also on a positive real parameter the existence of a sequence of critical points according to motreanu and panagiotopoulos minimax theorems and qualitative properties of the solutions of hemivariational inequalities nonconvex optimization applications vol 29 kluwer dordrecht 1998 chap 3 is established by mainly adapting a new technique due to ricceri 2000 j comput appl math 113 401 410 two applications are then presented both of them treat the neumann problem for an elliptic variational hemivariational inequality with p laplacian

multiple solutions for a coupled system of nonlinear fractional differential equations via variational methods in this paper a coupled system of nonlinear fractional differential equations is considered the existence of at least three distinct weak solutions is obtained by means of the variational methods and the critical point theory due to bonanno and marano in addition an example is presented to illustrate the feasibility and effectiveness of the main results

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

existence of three solutions for a non homogeneous neumann problem through orlicz sobolev spaces abstract the aim of this paper is to establish a multiplicity result for an eigenvalue non homogeneous neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition precisely a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate orlicz sobolev space

non trivial solutions for nonlinear fourth order elastic beam equations abstract the existence of at least one non trivial solution to a boundary value problem for fourth order elastic beam equations under a non standard growth condition of the nonlinear term is established our approach is based on a local minimum theorem for differentiable functionals

multiplicity results for semilinear elliptic problems at resonance and with jumping nonlinearities abstract in the present paper we develop a method to deal with multiple existence of solutions of nonlinear elliptic problems and give some multiple existence results for elliptic boundary value problems at resonance and problems with jumping nonlinearities

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

three weak solutions for elliptic dirichlet problems an existence result of three non zero solutions for non autonomous elliptic dirichlet problems under suitable assumptions on the nonlinear term is presented the approach is based on a recent three critical points theorem for differentiable functionals

three solutions to a perturbed nonlinear discrete dirichlet problem using critical point theory we study the existence of at least three solutions for a perturbed nonlinear dirichlet boundary value problem for difference equations depending on two positive parameters

infinitely many arbitrarily small positive solutions for the dirichlet problem involving the p laplacian in this paper we present a result of existence of infinitely many arbitrarily small positive solutions to the following dirichlet problem involving the p laplacian where r n is a bounded open set with sufficiently smooth boundary p 1 0 and f r r is a caratheodory function satisfying the following condition there exists t 0 such that precisely our result ensures the existence of a sequence of a e positive weak solutions to the above problem converging to zero in l

on the multiplicity of the solutions of the equation δu λ f u abstract let be a bounded open subset of r n we discuss conditions on the continuous function f r r ensuring that the problem u f u admits unboundedly many weak solutions in h 1 0 for any positive real

non differentiable functionals and applications to elliptic problems with discontinuous nonlinearities abstract multiple critical points theorems for non differentiable functionals are established applications both to elliptic variational hemivariational inequalities and eigenvalue problems with discontinuous nonlinearities are then presented

dynamic three dimensional computations for solids with variable nodal connectivity for severe distortions this paper presents a three dimensional algorithm for dynamic lagrangian computations for solids with variable nodal connectivity to allow for severe distortions the nodes are analogous to flexible spheres when they move closer together than their equilibrium distance they generate compressive repulsive forces conversely when they move apart they generate tensile attractive forces material strength effects are also included because a node can be affected only by its neighbour nodes the approach has been designated the nabor approach the distinguishing feature of this technique is that it is possible to have variable connectivity a node can acquire new neighbours thus allowing all forms of distortion the three dimensional nabor algorithm has been incorporated as an option into the explicit finite element code epic 3 by using both the nabor grid and the traditional epic 3 finite element grid together it is possible to perform lagrangian computations for a wider range of problems

on a new class of elliptic systems with nonlinearities of arbitrary growth abstract we guarantee the existence of infinitely many different pairs of solutions to the system u v p in v f u in u v 0 on where 0 p 2 n 2 is a bounded domain in r n and the continuous nonlinear term f has an unusual oscillatory behavior the sequence of solutions tends to zero resp infinity with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity resp at zero whenever f oscillates near zero resp at infinity our results provide the first applications of ricceri s variational principle in the theory of coupled elliptic systems

existence and multiplicity results to neumann problems for elliptic equations involving the p laplacian abstract in this paper existence results of positive solutions to a neumann problem involving the p laplacian are established multiplicity results are also pointed out the approach is based on variational methods

existence results for some anisotropic dirichlet problems abstract this paper concerns with a class of elliptic anisotropic dirichlet problems depending of one real parameter on bounded euclidean domains our approach is based on variational and topological methods more concretely along the paper we show the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated pucci and serrin theorem in addition to a local minimum result for differentiable functionals due to ricceri this abstract approach has been developed for equations on carnot groups see 15

infinitely many solutions for the dirichlet problem involving the p laplacian abstract using a recent variational principle of ricceri we present a result of existence of infinitely many solutions for the dirichlet problem involving the p laplacian

positive solutions of elliptic problems with locally oscillating nonlinearities abstract we prove the existence of two unbounded sequences of strictly positive solutions obtained respectively as minimum and saddle points of the associated action functional of the elliptic problem u f x u in u 0 on assuming that an oscillatory behaviour at of s 2 0 s f x d occurs locally in