Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 16, pp. 1-5.

Title: Existence of entire positive solutions for a class of
       semilinear elliptic systems
       
Author: Zhijun Zhang (Yantai Univ., Shandong, China)

Abstract:
 Under simple conditions on $f_i$ and $g_i$, we show
 the existence of entire positive radial solutions for
 the semilinear elliptic system
 $$\displaylines{
  \Delta u =p(|x|)f_1(v)f_2(u)\cr
  \Delta v =q(|x|)g_1(v)g_2(u),
 }$$
 where $x\in \mathbb{R}^N$, $N\geq 3$, and p,q are continuous
 functions.

Submitted October 22, 2009. Published January 27, 2010.
Math Subject Classifications: 35J55, 35J60, 35J65.
Key Words: Semilinear elliptic systems; entire solutions; existence.