Electron. J. Diff. Equ., Vol. 2014 (2014), No. 53, pp. 1-11.

Infinitely many solutions for elliptic boundary value problems with sign-changing potential

Wen Zhang, Xianhua Tang, Jian Zhang

Abstract:
In this article, we study the elliptic boundary value problem
$$\displaylines{ -\Delta u+a(x)u=g(x, u) \quad \text{in } \Omega,\cr u = 0\quad \text{on } \partial \Omega, }$$
where $ \Omega\subset \mathbb{R}^N$ $(N\geq3)$ is a bounded domain with smooth boundary $ \partial\Omega$ and the potential $a(x)$ is allowed to be sign-changing. We establish the existence of infinitely many nontrivial solutions by variant fountain theorem developed by Zou for sublinear nonlinearity.

Submitted September 8, 2013. Published February 21, 2014.
Math Subject Classifications: 35J25, 35J60.
Key Words: Semilinear elliptic equations; boundary value problems; sublinear; sign-changing potential.

Show me the PDF file (243 KB), TEX file, and other files for this article.

Wen Zhang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: zwmath2011@163.com
Xianhua Tang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: tangxh@mail.csu.edu.cn
Jian Zhang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: zhangjian433130@163.com

Return to the EJDE web page