p(x)-Kirchhoff-type problem with no-flux boundary conditions and convection

Abstract

This article establishes the existence of a weak solution for a class of p(x)p\left(x)-Kirchhoff-type problem under no-flux boundary conditions with a reaction term depending also on the gradient convection. The proof of the main result is constructed by utilizing the theory of topological degree and the theory of generalized Sobolev spaces.

Keywords

• p(x)-kirchhoff-type problem
• variable exponent sobolev spaces
• weak solution
• topological degree theory
• 35j60
• 47j05
• 47h11