期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
卷 26, 期 1, 页码 135-149出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcds.2010.26.135
关键词
Klein-Gordon-Maxwell system; standing waves; electrostatic field
资金
- M.I.U.R. - P.R.I.N.
This paper is concerned with the Klein-Gordon-Maxwell system in a hounded space domain. We discuss the existence of standing waves psi = u(x)e(-iwt) in equilibrium with a purely electrostatic field E = -del phi(x). We assume homogeneous Dirichlet boundary conditions on u and non homogeneous Neumann boundary conditions on phi. In the linear case we prove the existence of a nontrivial solution when the coupling constant is sufficiently small. Moreover we show that a suitable nonlinear perturbation in the matter equation gives rise to infinitely many solutions. These problems have a variational structure so that we can apply global variational methods.
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