BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

doi:10.1016/S0252-9602(17)30011-5

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 405-424.doi: 10.1016/S0252-9602(17)30011-5

BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

巴娜¹, 代晋军²

1. School of Science, Hubei University of Technology, Wuhan 430068, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

收稿日期:2016-08-02 出版日期:2017-04-25 发布日期:2017-04-25
作者简介:Na BA,E-mail:bana1002@126.com;Jinjun DAI,E-mail:jjdai@mail.ccnu.edu.cn
基金资助:
Na Ba was supported by National Natural Science Foundation of China (11201132), Scientific Research Foundation for Ph.D of Hubei University of Technology (BSQD12065), and the Scientific Research Project of Education Department of Hubei Province (Q20151401).

BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

Na BA¹, Jinjun DAI²

1. School of Science, Hubei University of Technology, Wuhan 430068, China;
2. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China

Received:2016-08-02 Online:2017-04-25 Published:2017-04-25
Supported by:
Na Ba was supported by National Natural Science Foundation of China (11201132), Scientific Research Foundation for Ph.D of Hubei University of Technology (BSQD12065), and the Scientific Research Project of Education Department of Hubei Province (Q20151401).

摘要/Abstract

摘要：

We study the bound states to nonlinear Schrödinger equations with electromagnetic fields ih (∂ψ/∂t)=(h/i▽-A(x))²ψ + V(x)ψ-K(x)|ψ|^p-1ψ=0, on R₊×R^N. Let G (x)=[V (x)]^{(p+1)/(p-1)-N/2}[K(x)]^-2/(p-1) and suppose that G(x) has k local minimum points. For h > 0 small, we find multi-bump bound states ψ_h(x, t)=e^-iEt/h u_h(x) with u_h concentrating at the local minimum points of G(x) simultaneously as h → 0. The potentials V (x) and K(x) are allowed to be either compactly supported or unbounded at infinity.

关键词: Multi-bump solutions, nonlinear Schrödinger equation, electromagnetic fields, potentials compactly supported or unbounded at infinity

Abstract:

Key words: Multi-bump solutions, nonlinear Schrödinger equation, electromagnetic fields, potentials compactly supported or unbounded at infinity

巴娜, 代晋军. BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS[J]. 数学物理学报(英文版), 2017, 37(2): 405-424.

Na BA, Jinjun DAI. BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS[J]. Acta mathematica scientia,Series B, 2017, 37(2): 405-424.

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BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

BOUND STATES OF SCHRÖDINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

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