Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 121, pp. 1-11.

Title: Multiple solutions for a elliptic system in exterior domain
  
Authors: Huijuan Gu  (Jiangxi Normal Univ., China)
         Jianfu Yang (Jiangxi Normal Univ., China)
	 Xiaohui Yu  (Central Univ. of Finance and Econ., Beijing, China)
 
Abstract:
 In this paper, we study the existence
 of solutions for the nonlinear elliptic system
 $$\displaylines{
 -\Delta u+u=|u|^{p-1}u+\lambda v  \quad \hbox{in }  \Omega,    \cr
 -\Delta v+v=|v|^{p-1}v+\lambda u  \quad \hbox{in }  \Omega,    \cr
 u=v=0  \quad \hbox{on }  \partial\Omega,
 }$$
 where $\Omega$ is a exterior domain in $\mathbb{R}^N$, $N\geq 3$.
 We show that the system possesses at least one nontrivial positive solution.
 
Submitted June 28, 2008. Published August 28, 2008.
Math Subject Classifications: 35J50, 35B32.
Key Words: Exterior domain; nonlinear elliptic system; existence result.