Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 53, pp. 1-11.
Title: Infinitely many solutions for elliptic boundary
         value problems with sign-changing potential

Authors: Wen Zhang    (Central South Univ., Hunan, China)
         Xianhua Tang (Central South Univ., Hunan, China)
         Jian Zhang   (Central South Univ., Hunan, China)

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.