Existence results for Schrödinger $p(x)$-Laplace equations involving critical growth in ${\mathbb{R}}^N$

Abstract

We establish some existence results for Schrödinger $p(x)$-Laplace equations in ${\mathbb{R}}^N$ with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space ${\mathbb{R}}^N$. The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.

26 pages