Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 81, pp. 1-11.

Title: Existence results for strongly indefinite elliptic systems
  
Authors: Jianfu Yang (Normal Univ., Nanchang, China)
         Ying Ye    (Jiangxi Normal Univ., Nanchang, China)
	 Xiaohui Yu (Central Univ. Finance and Economics, Beijing, China)

Abstract: 
 In this paper, we show the existence of solutions for
 the strongly indefinite elliptic system
 $$\displaylines{
 -\Delta u=\lambda u+f(x,v)  \quad\hbox{in }\Omega, \cr
 -\Delta v=\lambda v+g(x,u) \quad\hbox{in }\Omega, \cr
 u=v=0,  \quad\hbox{on }\partial\Omega,
 }$$
 where $\Omega$ is a bounded domain in $\mathbb{R}^N\; (N\geq 3)$ with smooth
 boundary, $\lambda_{k_0}<\lambda<\lambda_{k_0+1}$, where $\lambda_k$ is
 the $k$th eigenvalue of $-\Delta$ in $\Omega$ with zero Dirichlet
 boundary condition. Both cases when  $f,g$ being superlinear and 
 asymptotically linear at infinity are  considered.
 
Submitted April l7, 2008. Published May 28, 2008.
Math Subject Classifications: 35J20,3 5J25.
Key Words: Strongly indefinite elliptic system; existence.