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On Some $\overrightarrow {p(x)}$ Anisotropic Elliptic Equations in Unbounded Domain
Ahmed Aberqi
,
Benali Aharrouch
,
Jaouad Bennouna
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.