Positive solutions for nonlinear elliptic systems

Abstract

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 $H,K: mathbb{R}^nimes[0,infty)imes[0,infty)o[0,infty)$ 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.

Keywords

• Semilinear elliptic systems
• positive large solution
• positive bounded solution