Using Moser’s iteration method, we investigate the problem of removable isolated singularities for elliptic equations with p(x)-type nonstandard growth. We give a sufficient condition for removability of singularity for the equations in the framework of variable exponent Sobolev spaces.

This paper is concerned with the following Dirichlet problem for a quasilinear elliptic system with variable growth: –divσ (x,u(x),Du(x)) = f in , u(x) = 0 on ∂ , where ⊂Rn is a bounded domain. By means of the Young measure and the theory of variable exponent Sobolev spaces, we obtain the existence of solutions in W 0 ( ,R m) for each f ∈ (W 0 ( ,Rm))∗.

This paper deals with the existence of weak solutions for some nonlocal problem involving the p (x)Laplace operator. Using a direct variational method and the theory of the variable exponent Sobolev spaces, we set some conditions that ensures the existence of nontrivial weak solutions.

Let s ∈ R and p ≥ 1; the Sobolev space Lp,s(Rd) is the space of tempered distributions f such that (Id−∆)s/2 f ∈ Lp, where (Id−∆)s/2 is the Fourier multiplier by (1 + |ξ|2)s/2. If s > d/p, then Lp,s is composed of continuous functions; more precisely, the Sobolev embeddings state that Lp,s↩Cs−d/p, see [24, Chapter 11]. In order to state in which sense this embedding is sharp, we need to recall ...

in this paper, we study the nehari manifold and its application on the following navier boundary valueproblem involving the p-biharmonic          0, on( ) 1 ( , ) , in , 2*2u uf x u u upu u p q where  is a bounded domain in rn with smooth boundary  . we prove that the problem has atleast two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset o...

In this paper we are concerned with the study of a class of quasilinear elliptic differential inclusions involving the anisotropic − →p (·)-Laplace operator, on a bounded open subset of Rn which has a smooth boundary. The abstract framework required to study this kind of differential inclusions lies at the interface of three important branches in analysis: nonsmooth analysis, the variable expon...