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.

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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

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