Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 207, pp. 1-9.

Title: Multiple solutions for semilinear elliptic equations with
       sign-changing potential and nonlinearity 

Authors: Dongdong Qin (Central South Univ., Changsha, Hunan, China)
         Xianhua Tang (Central South Univ., Changsha, Hunan, China)
         Jiang Zhang  (Central South Univ., Changsha, Hunan, China)

Abstract:
 In this article, we study the multiplicity of solutions
 for the semilinear elliptic equation
  $$\displaylines{
    -\Delta u+a(x)u=f(x, u), \quad  x\in \Omega,\cr
    u=0,  \quad  x \in \partial\Omega,
   }$$
 where $ \Omega\subset \mathbb{R}^N$ $(N\geq3)$, the potential a(x)
 satisfies suitable integrability conditions, and the primitive of
 the nonlinearity f is of super-quadratic growth near infinity
 and is allowed to change sign.  Our super-quadratic conditions are weaker
 the usual super-quadratic conditions.

Submitted April 22, 2013. Published September 18, 2013.
Math Subject Classifications: 35J25, 35J60, 58E05.
Key Words: Semilinear elliptic equation; super-quadratic; 
           sign-changing potential.