Electron. J. Diff. Equ., Vol. 2013 (2013), No. 207, pp. 1-9.

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

Dongdong Qin, Xianhua Tang, Jiang Zhang

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.

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Dongdong Qin
School of Mathematics and Statistics, Central South University
Changsha, 410083 Hunan, China
email: qindd132@163.com
Xianhua Tang
School of Mathematics and Statistics, Central South University
Changsha, 410083 Hunan, China
email: tangxh@mail.csu.edu.cn
Jiang Zhang
School of Mathematics and Statistics, Central South University
Changsha, 410083 Hunan, China
email: zhangjian433130@163.com

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