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

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