An existence result for a $(p(x), q(x))$-Kirchhoff type system with Dirichlet boundary conditions via topological degree method

This paper focuses on the existence of at least one weak solution for a nonlocal elliptic system of $(p(x), q(x))$-Kirchhoff type with Dirichlet boundary conditions. The results are obtained by applying the topological degree method of Berkovits applied to an abstract Hammerstein equation associated to our system and also by the theory of the generalized Sobolev spaces.