Existence and multiplicity of solutions for nonlocal Neumann problem with non-standard growth

Abstract

In this paper, we are concerned with questions of existence of solution for a nonlocal and non-homogeneous Neumann boundary value problems involving the $p(x)$-Laplacian in which the non-linear terms have critical growth. The main tools we will use are the generalized Sobolev spaces and the Mountain Pass Theorem.