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.
Francisco Julio S.A. Corrêa. Augusto César dos Reis Costa. "Existence and multiplicity of solutions for nonlocal Neumann problem with non-standard growth." Differential Integral Equations 29 (3/4) 377 - 400, March/April 2016. https://doi.org/10.57262/die/1455806029