No abstract

In this paper, we examine the existence of entropy solutions for some nonlinear p(x)−elliptic equation of the type:where A is an operator of Leray-Lions type acting from W 1,p(x) 0(Ω) into its dual. The strongly nonlinear term H is assumed only to satisfy some nonstandard growth condition with respect to |∇u|. We assume that φ(·) ∈ C 0 (IR, IR N ) and µ belongs to M b 0 (Ω).

In this paper, we consider the Neumann p(x)-elliptic problems of the typeWe prove the existence of infinitely many weak solutions in the anisotropic variable exponent Sobolev space W 1, p(x) ( ) under some hypotheses.

This work is devoted to the study of the spectrum for p-biharmonic operator with an indefinite weight in a bounded domain.

AbstractIn this work, we investigate the spectrum denoted by Λ for the {p(x)}-biharmonic operator involving the Hardy term. We prove the existence of at least one non-decreasing sequence of positive eigenvalues of this problem such that {\sup\Lambda=+\infty}. Moreover, we prove that {\inf\Lambda>0} if and only if the domain Ω satisfies the {p(x)}-Hardy inequality.