The 2-dimensional nonlinear Schrödinger–Maxwell system

Abstract

In this paper we carry on the study of a system recently introduced by the first author as the planar version of the well known electrostatic Schrödinger–Maxwell equations. In the positive potential case, we exhibit situations where the existence of solutions depends on the strength of the coupling, being this one modulated by a parameter. We also present some results in the case of a sign-changing potential.