A system of two elliptic equations with nonlinear convection and coupled reaction terms

Abstract

The present paper is concerned with the existence of solutions for a class of elliptic systems involving nonlinearities of the Keller- Osserman type and combined with the convection terms. Firstly, we establish a result involving sub and super-solution for a class of elliptic systems whose nonlinearity may depend of the gradient of the solution. This result permits the study of the existence of blow-up solution for a large class of systems.