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

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.