Electron. J. Diff. Equ., Vol. 2014 (2014), No. 150, pp. 1-13.

Multiple solutions for Schrodinger-Maxwell systems with unbounded and decaying radial potentials

Fangfang Liao, Xiaoping Wang, Zhigang Liu

Abstract:
This article concerns the nonlinear Schrodinger-Maxwell system
$$\displaylines{ -\Delta u +V(|x|)u +Q(|x|)\phi u=Q(|x|) f(u),\quad \hbox{in } \mathbb{R}^3\cr -\Delta \phi =Q(|x|) u^{2}, \quad \hbox{in } \mathbb{R}^3 }$$
where V and Q are unbounded and decaying radial. Under suitable assumptions on nonlinearity f(u), we establish the existence of nontrivial solutions and a sequence of high energy solutions in weighted Sobolev space via Mountain Pass Theorem and symmetric Mountain Pass Theorem.

Submitted March 14, 2014. Published June 27, 2014.
Math Subject Classifications: 35J20, 35J60.
Key Words: Schrodinger-Maxwell system; unbounded or decaying potential; weighted Sobolev space; mountain pass theorem

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Fangfang Liao
School of Mathematics and Statistics, Central South University
Changsha, 410083, Hunan, China.
Department of Mathematics, Xiangnan University
Chenzhou, 423000, Hunan, China
email: liaofangfang1981@126.com
Xiaoping Wang
Department of Mathematics, Xiangnan University
Chenzhou, 423000, Hunan, China
email: wxp31415@163.com
Zhigang Liu
Department of Mathematics, Xiangnan University
Chenzhou, 423000, Hunan, China
email: liuzg22@sina.com

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