Existence and multiplicity of solutions for nonlocal Neumann problem with non-standard growth. (English) Zbl 1374.35160

Corrêa, Francisco Julio S. A.; Costa, Augusto César dos Reis

Differ. Integral Equ. 29, No. 3-4, 377-400 (2016).

Summary: 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.

MSC:

35J60	Nonlinear elliptic equations
35J70	Degenerate elliptic equations
58E05	Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces

Keywords:

critical growth; integral term; \(p(x)\)-Laplacian