The 2-dimensional nonlinear Schrödinger–Maxwell system. (May 2023)

• Record Type: Journal Article
• Authors: Azzollini, Antonio; Pimenta, Marcos T.O.
• Is Part Of: Nonlinear analysis. Volume 230(2023)
• Publication Date: 2023-05
• Subjects: 35J50 -- 35Q40; Schrödinger–Maxwell system -- Logarithmic convolution potential -- Elliptic systems; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2023.113224
• Languages: English
• ISSNs: 0362-546X

Abstract

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.