Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 239, pp. 1-10.
Title: Positive solutions for nonlinear elliptic systems
Author: Adel Ben Dekhil (Univ. de Tunis El Manar, Tunis, Tunisia)
Abstract:
In this article, we study the existence of positive solutions for the system
$$\displaylines{
\Delta u=H(x,u,v),\cr
\Delta v=K(x,u,v),\hbox{in }\mathbb{R}^n\; (n\geq 3),
}$$
where $H,K: \mathbb{R}^n\times[0,\infty)\times[0,\infty)\to[0,\infty)$
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.
Submitted October 14, 2012. Published December 28, 2012.
Math Subject Classifications: 35B08, 35B09, 35J47.
Key Words: Semilinear elliptic systems; positive large solution;
positive bounded solution.