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

Paulo C. Carriao, Patricia L. Cunha, Olimpio H. Miyagaki

Published 2009-09-16Version 1

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.