Existence results for the Klein-Gordon-Maxwell equations in higher dimensions with critical exponents

Pages: 709 - 718, Volume 10, Issue 2, March 2011

doi:10.3934/cpaa.2011.10.709       Abstract        References        Full Text (353.6K)       Related Articles

Paulo Cesar Carrião - Departamento de Matematica, Universidade Federal de Minas Gerais, 31270-010 Belo Horizonte-MG, Brazil (email)
Patrícia L. Cunha - Departamento Matemática, Universidade Federal de São Carlos, São Carlos, SP 13565-905, Brazil (email)
Olímpio Hiroshi Miyagaki - Departamento de Matematica, Universidade Federal de Vicosa, 36371-000 Vicosa-MG, Brazil (email)

Abstract: In this paper we study the existence of radially symmetric solitary waves in $R^N$ for the nonlinear Klein-Gordon equations coupled with the Maxwell's equations when the nonlinearity exhibits critical growth. The main feature of this kind of problem is the lack of compactness arising in connection with the use of variational methods.

Keywords:  Klein-Gordon-Maxwell system, radially symmetric solution, critical growth.
Mathematics Subject Classification:  Primary: 35J47, 35J50, 35B33; Secondary: 81Q05, 34B18.

Received: May 2010;      Revised: August 2010;      Published: December 2010.

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