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Acta Applicandae Mathematicae

, Volume 130, Issue 1, pp 237–250 | Cite as

Multiplicity of Solutions for a Nonlinear Klein-Gordon-Maxwell System

  • Xiaoming HeEmail author
Article

Abstract

In this paper we study the nonlinear Klein-Gordon-Maxwell system
$$\left \{\begin{array}{l@{\quad}l} -\Delta u+V(x)u-(2\omega+\phi)\phi u=f(x,u),&x\in{\mathbb{R}}^3,\\ \Delta \phi=(\omega+\phi)u^2,&x\in{\mathbb{R}}^3. \end{array} \right . $$
By means of a variant fountain theorem and the symmetric mountain pass theorem, we obtain the existence of infinitely many large energy solutions.

Keywords

Klein-Gordon-Maxwell equation Large energy solutions Variational methods 

Mathematics Subject Classification (2000)

35J60 35Q40 

Notes

Acknowledgements

The author is very grateful to the anonymous referee for his/her careful reading the manuscript and valuable comments. This work was supported by NSFC Grants (11271386).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.College of SciencesMinzu University of ChinaBeijingP.R. China

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