Electron. J. Diff. Equ., Vol. 2016 (2016), No. 26, pp. 1-9.

Multiple solutions for semilinear Schrodinger equations with electromagnetic potential

Wen Zhang, Xianhua Tang, Jian Zhang

Abstract:
In this article, we consider the existence of infinitely many nontrivial solutions for the following semilinear Schr\"odinger equation with electromagnetic potential
$$ \big(-i\nabla+A(x)\big)^2u+V(x)u=f(x,|u|)u,\quad\text{in } \mathbb{R}^N $$
where i is the imaginary unit, V is the scalar (or electric) potential, A is the vector (or magnetic) potential. We establish the existence of infinitely many solutions via variational methods.

Submitted October 7, 2015. Published January 15, 2016.
Math Subject Classifications: 58E05, 35J20.
Key Words: Semilinear Schrodinger equation; magnetic potential; variational methods.

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Wen Zhang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: zwmath2011@163.com
Xianhua Tang
School of Mathematics and Statistics
Central South University
Changsha, 410083 Hunan, China
email: tangxh@mail.csu.edu.cn
Jian Zhang
School of Mathematics and Statistics
Hunan University of Commerce
Changsha, 410205 Hunan, China
email: zhangjian433130@163.com

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