Existence of ground state solutions to a generalized quasilinear Schrödinger-Maxwell system

Abstract

In this paper, a class of generalized quasilinear Schrödinger-Maxwell systems is considered. Via the mountain pass theorem, we conclude the existence of positive ground state solutions when the potential may vanish at infinity and the nonlinear term has a quasicritical growth. During this process, we use the Coulomb energy studied by Ruiz [Arch. Ration. Mech. Anal. 198(1), 349–368 (2010)] and establish a convergency theorem to overcome the lack of compactness caused by the potential which may vanish at infinity.