Electron. J. Diff. Eqns., Vol. 2005(2005), No. 129, pp. 1-11.

An application of the Lyapunov-Schmidt method to semilinear elliptic problems

Quoc Anh Ngo

In this paper we consider the existence of nonzero solutions for the undecoupling elliptic system
 -\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.

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Quoc Anh Ngo
Department of Mathematics, Mechanics and Informatics
College of Science, Vietnam National University
Hanoi, Vietnam
email: bookworm_vn@yahoo.com   anhngq@yahoo.com.vn

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