On a new p(x)-Kirchhoff type problems with p(x)-Laplacian-like operators and Neumann boundary conditions

Abstract

In this paper we study a Neumann boundary value problem of a new p(x)-Kirchhoff type problems driven by p(x)-Laplacian-like operators. Using the theory of variable exponent Sobolev spaces and the method of the topological degree for a class of demicontinuous operators of generalized (S+) type,weprove theexistenceofaweak solutionsof this problem. Our results are a natural generalisation of some existing ones in the context of p(x)-Kirchhoff type problems.

Keywords

• p(x)-kirchhoff type problems
• p(x)-laplacian-like operators
• neumann boundary conditions
• topological degree methods
• weak solutions
• variable exponent sobolev spaces
• 35j60
• 35j70
• 35d30
• 47h11