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Positive ground state solutions for the critical Klein-Gordon-Maxwell system with potentials. (English) Zbl 1238.35109

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.

MSC:

35Q40 PDEs in connection with quantum mechanics
35Q61 Maxwell equations
35B09 Positive solutions to PDEs
35J50 Variational methods for elliptic systems
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References:

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