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

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.

Show me the PDF file (222K), TEX file, and other files for this article.

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

Return to the EJDE web page