A local mountain pass approach for a class of fractional NLS equations with magnetic fields. (January 2020)

• Record Type: Journal Article
• Authors: Ambrosio, Vincenzo
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 47G20 -- 35R11 -- 35A15 -- 58E05; Magnetic fractional Laplacian -- Variational methods -- Fractional magnetic Kato's inequality; 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.2019.111622
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We complete the recent study started in Ambrosio (2019) concerning the existence and concentration phenomenon of complex-valued solutions for a class of nonlinear Schrödinger equations driven by the fractional magnetic Laplacian ( − Δ ) A s . The proofs are obtained by combining suitable variational methods with a Kato's approximation argument for ( − Δ ) A s . The approach developed here can be also used to consider other fractional magnetic problems like fractional magnetic Choquard equations, fractional magnetic Kirchhoff problems and fractional magnetic Schrödinger–Poisson equations, in which local conditions on the potential are assumed.