Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 129, pp. 1-11.

Title: An application of the Lyapunov-Schmidt method to semilinear
       elliptic problems
       
Author: Quoc Anh Ngo (Vietnam National Univ., Hanoi, Vietnam)

Abstract: 
 In this paper we consider the existence of nonzero solutions for
 the undecoupling elliptic system
 $$\displaylines{
 -\Delta u=\lambda u+\delta v+f(u,v), \cr
 -\Delta v=\theta u+ \gamma v+g(u,v),
 }$$
 on a bounded domain of $\mathbb{R}^n$, with zero Dirichlet boundary
 conditions. We use the Lyapunov-Schmidt method and the fixed-point
 principle.
 
Submitted July 12, 2005. Published November 23, 2005.
Math Subject Classifications: 35J50, 35J55.
Key Words: Semilinear; elliptic system; Lyapunov; Schmidt;
           fixed-point principle.