Existence of solutions of sublinear elliptic systems with quadratic growth in the gradient

In this paper, we deal with the following sublinear elliptic system: $${{\left\{\begin{array}{ll}-\Delta u + u + |\nabla u|^2 = a(x)|v|^p+ f,\quad x \in \mathbb{R}^N,\\ -\Delta v + v + |\nabla v|^2 = b(x)|u|^q+ g,\quad x \in \mathbb{R}^N,\\\end{array}\right.}}$$ where 0 <  p <  1 and 0 <  q <  1. Under suitable assumptions on the terms a, b, f and g and by using the Schauder fixed point theorem, we obtain a solution for an approximated system. The limit of the approximated solutions is a nonnegative solution.