Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 224, pp. 1-9.
Title: Infinitely many large energy solutions of superlinear
Schrodinger-Maxwell equations
Authors: Lin Li (Southwest Univ., Chongqing, China)
Shang-Jie Chen (Chongqing Tech. and Business Univ., China)
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.