Electron. J. Diff. Equ., Vol. 2012 (2012), No. 224, pp. 1-9.

Infinitely many large energy solutions of superlinear Schrodinger-Maxwell equations

Lin Li, Shang-Jie Chen

Abstract:
In this article we study the existence of infinitely many large energy solutions for the superlinear Schrodinger-Maxwell equations
$$\displaylines{ -\Delta u+V(x)u+ \phi u=f(x,u) \quad \hbox{in }\mathbb{R}^3,\cr -\Delta \phi=u^2, \quad \hbox{in }\mathbb{R}^3, }$$
via the Fountain Theorem in critical point theory. In particular, we do not use the classical Ambrosetti-Rabinowitz condition.

Submitted July 10, 2012. Published December 11, 2012.
Math Subject Classifications: 35J35, 35J60, 47J30, 58E05.
Key Words: Schrodinger-Maxwell equations; superlinear; fountain theorem; variational methods.

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Lin Li
School of Mathematics and Statistics
Southwest University, Chongqing 400715, China
Department of Science, Sichuan University of Science and Engineering
Zigong 643000, China
email: lilin420@gmail.com
Shang-Jie Chen
School of Mathematics and Statistics
Chongqing Technology and Business University
Chongqing 400067, China
email: 11183356@qq.com

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