Systems of Kirchhoff type equations with gradient dependence in the reaction term via subsolution-supersolution method

Abstract

We consider a Dirichlet problem for a system of equations involving Kirchhoff type $ p_i $-Laplacian differential operators and exhibiting gradient dependence in the reaction term (convection). Using the subsolution-supersolution method, we establish the existence of weak solutions into suitable ordered intervals. Following unified approach, we also provide a comparison argument to obtain positive solutions of certain models.