Existence of weak solutions to a p(x)-Kirchhoff type problems involving the p(x)-Laplacian-like operators

Abstract

This paper investigates the existence of weak solutions for a Dirichlet boundary value problem of $p(x)$-Kirchhoff type driven by $p(x)$-Laplacian-like operators, arising from the capillarity phenomena. The existence is proved by using the topological degree for a class of demicontinuous operators of generalized $(S_{+})$ type and the theory of variable-exponent Sobolev spaces. Our result extends some recent work in the literature.