Positive ground state solutions for the critical Klein–Gordon–Maxwell system with potentials

This paper deals with the Klein–Gordon–Maxwell system when the nonlinearity exhibits critical growth. We prove the existence of positive ground state solutions for this system when a periodic potential V is introduced. The method combines the minimization of the corresponding Euler–Lagrange function...

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Bibliographic Details
Published in:Nonlinear analysis 2012-06, Vol.75 (10), p.4068-4078
Main Authors: Carrião, Paulo C., Cunha, Patrícia L., Miyagaki, Olímpio H.
Format: Article
Language:English
Subjects:
Critical growth
Ground state
Ground state solutions
Manifolds
Minimization
Nonlinearity
Optimization
Variational methods
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Summary:This paper deals with the Klein–Gordon–Maxwell system when the nonlinearity exhibits critical growth. We prove the existence of positive ground state solutions for this system when a periodic potential V is introduced. The method combines the minimization of the corresponding Euler–Lagrange functional on the Nehari manifold with the Brézis and Nirenberg technique.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2012.02.023