The 2-dimensional nonlinear Schrodinger-Maxwell system

TL;DR

This paper investigates a 2D nonlinear Schrödinger-Maxwell system, analyzing how solution existence depends on coupling strength and potential sign, contributing new insights into planar electrostatic quantum models.

Contribution

It introduces the first detailed analysis of the 2D Schrödinger-Maxwell system, highlighting the impact of coupling strength and potential sign on solution existence.

Findings

Existence of solutions depends on coupling strength in positive potential cases.

Solutions are affected by the sign-changing nature of the potential.

The study extends understanding of planar electrostatic Schrödinger-Maxwell equations.

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 Schr\"odinger - 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.