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

Abstract

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.

Keywords

• Klein-Gordon-Maxwell
• positive solution
• ground state
• vanishing potential