A local mountain pass approach for a class of fractional NLS equations with magnetic fields

被引：7

作者：

Ambrosio, Vincenzo ^{[1
]}

机构：

[1] Univ Politecn Marche, Dipartimento Ingn Ind & Sci Matemat, Via Brecce Bianche 12, I-60131 Ancona, Italy

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2020年 / 190卷

关键词：

Magnetic fractional Laplacian; Variational methods; Fractional magnetic Kato's inequality; NONLINEAR SCHRODINGER-EQUATION; POSITIVE SOLUTIONS; EXISTENCE; OPERATORS;

D O I：

10.1016/j.na.2019.111622

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We complete the recent study started in Ambrosio (2019) concerning the existence and concentration phenomenon of complex-valued solutions for a class of nonlinear Schrodinger equations driven by the fractional magnetic Laplacian (-Delta)(A)(s). The proofs are obtained by combining suitable variational methods with a Kato's approximation argument for (-Delta)(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 Schrodinger-Poisson equations, in which local conditions on the potential are assumed. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：14

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