On Some \(\protect \overrightarrow {p(x)}\) 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 \({\varOmega }\subset \mathbb {R}^{N} (N \geq 2)\). We prove the existence of entropy solutions avoiding sign condition and coercivity on the lower order terms.