Electron. J. Diff. Eqns., Vol. 2008(2008), No. 121, pp. 1-11.

Multiple solutions for a elliptic system in exterior domain

Huijuan Gu, Jianfu Yang, Xiaohui Yu

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.

Show me the PDF file (252 KB), TEX file, and other files for this article.

Huijuan Gu
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: ruobing411@yahoo.com.cn
Jianfu Yang
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com
Xiaohui Yu
China Institute for Advanced Study
Central University of Finance and Economics
Beijing 100081, China
email: yuxiao_211@163.com

Return to the EJDE web page