A p(x)-Kirchhoff type problems involving the p(x)-Laplacian-like
operators with Dirichlet boundary conditions
Abstract
This paper deals with a class of $p(x)$-Kirchhoff type problems
involving the $p(x)$-Laplacian-like operators, arising from the
capillarity phenomena, depending on two real parameters with Dirichlet
boundary conditions. Using a topological degree for a class of
demicontinuous operators of generalized $(S_{+})$ type and the
theory of the variable exponent Sobolev spaces, we prove the existence
of weak solutions of this problem.