Electron. J. Differential Equations, Vol. 2017 (2017), No. 154, pp. 1-11.

Positive ground state solutions for quasicritical Klein-Gordon-Maxwell type systems with potential vanishing at infinity

Elson Leal de Moura, Olimpio Hiroshi Miyagaki, Ricardo Ruviaro

This article concerns the Klein-Gordon-Maxwell type system when the nonlinearity has a quasicritical growth at infinity, involving zero mass potential, that is, $V(x)\to 0$, as $|x|\to\infty$. The interaction of the behavior of the potential and nonlinearity recover the lack of the compactness of Sobolev embedding in whole space. The positive ground state solution is obtained by proving that the solution satisfies Mountain Pass level.

Submitted April 19, 2017. Published June 27, 2017.
Math Subject Classifications: 35A15, 35Q61, 35B38, 35B09.
Key Words: Klein-Gordon-Maxwell; positive solution; ground state; vanishing potential.

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Elson Leal de Moura
Universidade Federal dos Vales do Jequitinhonha e Mucuri
39803-371 Teófilo Otoni-MG, Brazil
email: elson.moura@ufvjm.edu.br
Olimpio Hiroshi Miyagaki
Universidade Federal de Juiz de Fora
Departamento de Matemática
36036-330 Juiz de Fora-MG, Brazil
email: ohmiyagaki@gmail.com
Ricardo Ruviaro
Universidade de Brasília
Departamento de Matemática
70910-900 Brasília-DF, Brazil
email: ruviaro@mat.unb.br

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