Positive solutions for nonlinear elliptic systems

In this article, we study the existence of positive solutions for the system $$displaylines{ Delta u=H(x,u,v),cr Delta v=K(x,u,v),hbox{in }mathbb{R}^n; (ngeq 3), }$$ where $H,K: mathbb{R}^n imes[0,infty) imes[0,infty) o[0,infty)$ are continuous functions satisfying $H(x,u,v)leq p_1(|x|)F(u+v)$ and $ K(x,u,v)leq q_1(|x|)G(u+v)$. In terms of the growth of the variable potential functions $p_1,q_1$ and the nonlinearities F and G, we establish some sufficient conditions for the existence of positive continuous solutions for this system and we discuss whether these solutions are bounded or blow up at infinity.