Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

Liping Wang; Chunyi Zhao

doi:10.1016/j.jde.2018.10.014

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

Liping Wang
, Chunyi Zhao^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove the existence of solutions to the nonlinear Schrödinger equation ε²(i∇+A)²u+V(y)u−|u|^p−1u=0 in R² with a magnetic potential A=(A₁,A₂). Here V represents the electric potential, the index p is greater than 1. Along some sequence {ε_n} tending to zero we exhibit complex-value solutions that concentrate along some closed curves.

Original language	English
Pages (from-to)	4800-4834
Number of pages	35
Journal	Journal of Differential Equations
Volume	266
Issue number	8
DOIs	https://doi.org/10.1016/j.jde.2018.10.014
State	Published - 5 Apr 2019

Keywords

High dimensional concentration
Magnetic potential
Nonlinear Schrödinger equation

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10.1016/j.jde.2018.10.014

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title = "Concentration on curves for a nonlinear Schr{\"o}dinger problem with electromagnetic potential",

abstract = "We prove the existence of solutions to the nonlinear Schr{\"o}dinger equation ε2(i∇+A)2u+V(y)u−|u|p−1u=0 in R2 with a magnetic potential A=(A1,A2). Here V represents the electric potential, the index p is greater than 1. Along some sequence \{εn\} tending to zero we exhibit complex-value solutions that concentrate along some closed curves.",

keywords = "High dimensional concentration, Magnetic potential, Nonlinear Schr{\"o}dinger equation",

author = "Liping Wang and Chunyi Zhao",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2019",

month = apr,

day = "5",

doi = "10.1016/j.jde.2018.10.014",

language = "英语",

volume = "266",

pages = "4800--4834",

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T1 - Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

AU - Wang, Liping

AU - Zhao, Chunyi

PY - 2019/4/5

Y1 - 2019/4/5

N2 - We prove the existence of solutions to the nonlinear Schrödinger equation ε2(i∇+A)2u+V(y)u−|u|p−1u=0 in R2 with a magnetic potential A=(A1,A2). Here V represents the electric potential, the index p is greater than 1. Along some sequence {εn} tending to zero we exhibit complex-value solutions that concentrate along some closed curves.

AB - We prove the existence of solutions to the nonlinear Schrödinger equation ε2(i∇+A)2u+V(y)u−|u|p−1u=0 in R2 with a magnetic potential A=(A1,A2). Here V represents the electric potential, the index p is greater than 1. Along some sequence {εn} tending to zero we exhibit complex-value solutions that concentrate along some closed curves.

KW - High dimensional concentration

KW - Magnetic potential

KW - Nonlinear Schrödinger equation

UR - https://www.scopus.com/pages/publications/85055525041

U2 - 10.1016/j.jde.2018.10.014

DO - 10.1016/j.jde.2018.10.014

M3 - 文章

AN - SCOPUS:85055525041

SN - 0022-0396

VL - 266

SP - 4800

EP - 4834

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 8

ER -

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

Abstract

Keywords

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