Elliptic Kirchhoff-type system with two convections terms and under Dirichlet boundary conditions

Abstract

This work discusses the existence of weak solutions for a system of Kirchhoff-type involving variable exponent (?1(m), ?2(m))-Laplacian operators and under the Dirichlet boundary conditions. Under appropriate hypotheses on the nonlinear terms and the Kirchhoff functions, the existence of weak solutions is obtained on the spaces W1,?1(m) 0 (D) ? W1,?2(m) 0 (D). The proof of the main result is based on a topological degree argument for a class of demicontinuous operators of (S+)-type.