existence of solutions for a p x kirchhoff type equation this paper is concerned with the existence and multiplicity of solutions to a class of p x kirchhoff type problem with dirichlet boundary data by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish conditions ensuring the existence and multiplicity of solutions for the problem

infinitely many solutions for a hemivariational inequality involving the p x laplacian abstract this paper deals with a hemivariational inequality involving the p x laplacian by using nonsmooth variational methods and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct non negative solutions of the problem in both cases one at the origin and the other at infinity under suitable hypotheses

estimating the frequency of a periodic function summary the problem of estimating the frequency and other parameters of a cyclical oscillation is considered where the data consists of a periodic function observed subject to stationary additive noise an estimation procedure is proposed and the asymptotic properties of the estimators established tests for unknown frequencies to be harmonics of a fundamental frequency are also developed and their asymptotic properties investigated the procedures are applied to observations on the variable star s carinae

renormalized solutions for nonlinear elliptic equations with variable exponents and l1 data abstract we prove existence and uniqueness of a renormalized solution to nonlinear elliptic equations with variable exponents and l 1 data the functional setting involves lebesgue sobolev space with variable exponents w 1 p

elliptic boundary value problems with nonstandard growth conditions abstract we study different boundary value problems to the p x laplacean equation namely of robin and signorini types we prove the existence and uniqueness of weak solutions to the problems under study and also their continuous dependence on the exponent data

existence of positive solutions for a class of p x laplacian systems abstract we mainly consider the system p x u f x v in p x v g x u in u v 0 on where r n is a bounded domain p x is a function which satisfies some conditions p x u div u p x 2 u is called p x laplacian we give the existence of positive solutions under some conditions in particular we do not assume radial symmetric conditions on the system

hartman type results for p t laplacian systems consider the weighted p t laplacian ordinary system w t u t p t 2u t w t f t u t 0 in a b u a u b 0 where f c a b rn rn w c a b r p c a b r and p t 1 for t a b it is proved that if r 0 such that f t u u 0 t a b u rn with u r then the problem has a solution u such that u t r for t a b as a corollary of this result taking w t tn 1 we obtain the existence of the radial solutions for the elliptic systems our result generalized the corresponding results obtained by hartman and mawhin

infinitely many solutions for a p x laplacian equation in rn abstract this paper deals with a p x laplacian equation in r n by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct homoclinic radially symmetric solutions whose w 1 p x r n norms tend to zero to infinity respectively under weaker hypotheses about nonlinearity at zero at infinity respectively

regularity results for a class of functionals with non standard growth we consider the integral functional under non standard growth assumptions that we call p x type namely we assume that a relevant model case being the functional under sharp assumptions on the continuous function p x 1 we prove regularity of minimizers energies exhibiting this growth appear in several models from mathematical physics

new diffusion models in image processing we give some diffusion models which can be used for restoration in image processing the proposed model is a combination of fast growth with respect to low gradient and slow growth when the gradient is large the existence theorem for solutions and some numerical results are given

existence and multiplicity of solutions for p x laplacian equations in rn abstract this paper investigates the existence and multiplicity of solutions for p x laplacian equations in r n

asymptotic stability for anisotropic kirchhoff systems we study the question of asymptotic stability as time tends to infinity of solutions of dissipative anisotropic kirchhoff systems involving the p x laplacian operator governed by time dependent nonlinear damping forces and strongly nonlinear power like variable potential energies this problem had been considered earlier for potential energies which arise from restoring forces whereas here we allow also the effect of amplifying forces global asymptotic stability can then no longer be expected and should be replaced by local stability the results are further extended to the more delicate problem involving higher order damping terms

on the c1 γ ω w2 2 ω regularity for a class of electro rheological fluids abstract we are concerned with a system of nonlinear partial differential equations with p x structure 1 p p x p 0 and no slip boundary conditions we prove the existence and uniqueness of a c 1 w 2 2 solution corresponding to small data without further restrictions on the bounds p p 0 in particular this result is applicable to the steady motion of shear dependent electro rheological fluids

existence of positive solutions for elliptic systems with nonstandard p x growth conditions via sub supersolution method abstract we mainly consider the system p x u f v in p x v g u in u v 0 on where p x c 1 r n is a radial symmetric function which satisfies sup p x and 1 inf p x sup p x where p x u div u p x 2 u is called p x laplacian b 0 r r n is a bounded radial symmetric domain where r is sufficiently large we prove the existence of a positive solution when lim u f m g u 1 p 1 u p 1 0 in particular we do not assume any sign condition on f 0 and g 0

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

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

the principle of concentration compactness in lp x spaces and its application abstract in this paper we establish a principle of concentration compactness in l p x spaces and apply it to obtain the existence of solutions for p x laplacian equations with critical growth

remarks on eigenvalue problems involving the p x laplacian abstract this paper deals with the eigenvalue problem involving the p x laplacian of the form div u p x 2 u u q x 2 u in u 0 on where is a bounded domain in r n p c 0 inf x p x 1 q l 1 q x q x e p x for x e is a positive constant p x is the sobolev critical exponent it is shown that for every t 0 the problem has at least one sequence of solutions u n t n t such that 1 p x u n t p x t and n t as n the principal eigenvalues for the problem in several important cases are discussed especially the similarities and the differences in the eigenvalue problem between the variable exponent case and the constant exponent case are exposed some known results on the eigenvalue problem are extended

existence of three solutions for p x laplacian equations abstract in this paper using b ricceri s three critical points theorem and variational methods we study the solutions of the p x laplacian equations with neumann or dirichlet boundary condition on a bounded domain and obtain three solutions under appropriate hypotheses

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 of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

limits as p x of p x harmonic functions abstract in this note we study the limit as p x of solutions to p x u 0 in a domain with dirichlet boundary conditions our approach consists in considering sequences of variable exponents converging uniformly to and analyzing how the corresponding solutions of the problem converge and which equation is satisfied by the limit

a multiplicity result for p x laplacian problem in rn abstract in this paper we discuss the solutions of the following p x laplacian problem div u p x 2 u u p x 2 u f x u x r n where 1 p p x p n based on the theory of the variable exponent sobolev spaces w 1 p x r n we get that there exist at least two non trivial weak solutions

infinitely many positive solutions for a p x kirchhoff type equation this paper is concerned with the existence of infinitely many positive solutions to a class of p x kirchhoff type problem by means of a direct variational approach and the theory of the variable exponent sobolev spaces we establish the existence of infinitely many distinct positive solutions whose w1 p x norms and l norms tend to zero under suitable hypotheses about nonlinearity

a model porous medium equation with variable exponent of nonlinearity existence uniqueness and localization properties of solutions abstract we study the localization properties of weak solutions to the dirichlet problem for the degenerate parabolic equation u t div u x t u f with variable exponent of nonlinearity we prove the existence and uniqueness of weak solutions and establish conditions on the problem data and the exponent x t sufficient for the existence of such properties as finite speed of propagation of disturbances the waiting time effect finite time vanishing of the solution it is shown that the solution may instinct in a finite time even if x 0 in the problem domain but max 0

on an open problem involving the p x laplacian a further study on the multiplicity of weak solutions to p x laplacian equations abstract by using a variational method and the truncation technique we show the multiplicity of weak solutions to a class of p x laplacian equations an open problem proposed by professor xianling fan is solved and more general results are given in this paper

existence of periodic solutions for p t laplacian systems abstract in this paper by using minimax methods in critical point theory we obtain some existence theorems for periodic solutions of p t laplacian system u t p t 2 u t f t u t 0 u 0 u t u 0 u t 0 and our results generalize some existed theorems

a free boundary problem for the p x laplacian abstract we consider the optimization problem of minimizing 1 p x u p x x u 0 d x in the class of functions w 1 p with u 0 w 0 1 p for a given 0 0 and bounded w 1 p is the class of weakly differentiable functions with u p x d x we prove that every solution u is locally lipschitz continuous that it is a solution to a free boundary problem and that the free boundary u 0 is a regular surface

overview of differential equations with non standard growth abstract differential equations with non standard growth have been a very active field of investigation in recent years in this survey we present an overview of the field as well as several of the most important results we consider both existence and regularity questions finally we provide a comprehensive list of papers published to date

gradient estimates for the p x laplacean system we prove calderon and zygmund type estimates for a class of elliptic problems whose model is the non homogeneous p x laplacean system div jduj p x 2 du div jf j p x 2 f

a local mountain pass theorem and applications to a double perturbed p x laplacian equations in this paper we prove a local mountain pass theorem without p s condition using this theorem and ricceri s variational principle we consider a double perturbed neumann problem with nonlinear boundary condition of the email protected p x u a x u p x 2u f x u email protected 1 x u email protected u p x email protected email protected email protected g x u email protected 2 x u email protected email protected least seven solutions are obtained under different assumptions

harnack estimates for quasi linear degenerate parabolic differential equations we establish the intrinsic harnack inequality for non negative solutions of a class of degenerate quasilinear parabolic equations including equations of the p laplacian and porous medium type it is shown that the classical harnack estimate while failing for degenerate parabolic equations it continues to hold in a space time geometry intrinsic to the degeneracy the proof uses only measure theoretical arguments it reproduces the classical moser theory for non degenerate equations and it is novel even in that context holder estimates are derived as a consequence of the harnack inequality the results solve a long standing problem in the theory of degenerate parabolic equations

existence of solutions for weighted p r laplacian impulsive system periodic like boundary value problems abstract this paper investigates the existence of solutions for weighted p r laplacian impulsive system periodic like boundary value problems our method is based on gaines and mawhin s coincidence degree theory we give the sufficient conditions of the existence of solutions

regularity results for a class of obstacle problems under nonstandard growth conditions abstract we prove regularity results for minimizers of functionals f u f x u d u d x in the class k u w 1 p x r u where r is a fixed function and f is quasiconvex and fulfills a growth condition of the type l 1 z p x f x z l 1 z p x with growth exponent p 1

nodal solutions of p x laplacian equations abstract the paper is concerned with the existence of nodal radial solutions for the p x laplacian equation div u p x 2 u a x u p x 2 u u q x 2 u in u w 0 1 p x it is proved that for any given nonnegative integer k the problem has a pair of solutions which has exactly k nodes when a p and q satisfy suitable conditions

eigenvalues of the p x laplacian neumann problems abstract we study the eigenvalues of the p x laplacian operator with zero neumann boundary condition on a bounded domain where p x is a continuous function defined on the domain with p x 1 we show that similarly to the p laplacian case the smallest eigenvalue of the problem is 0 and it is simple and the supremum of all the eigenvalues is infinity however unlike the p laplacian case for very general variable exponent p x the first eigenvalue is not isolated that is the infimum of all positive eigenvalues of the problem is 0 we also study some properties of the set of functions having p x average value zero

mathematical analysis of the propagation of elastic guided waves in heterogeneous media resume dans cet article nous nous interessons a la propagation d ondes elastiques dans des milieux isotropes heterogenes invariants par translation dans une direction nous faisons l analyse theorique de l existence d ondes guidees et de leurs proprietes en particulier les seuils ou frequences de coupures sont etudies en detail le principal outil mathematique est la theorie spectrale des operateurs autoadjoints et plus specialement le principe du max min