On some $\overrightarrow{p(x)}$ anisotropic elliptic equations in unbounded domain

Abstract

We study a class of nonlinear elliptic problems with Dirichlet conditions in the framework of the Sobolev anisotropic spaces with variable exponent, involving an anisotropic operator on an unbounded domain $\Omega \subset I{R}^N(N\ge 2)$. We prove the existence of entropy solutions avoiding sign condition and coercivity on the lowers order terms.

Accepted for publication in AMV