New type of solutions for the nonlinear Schrödinger equation in RN

Lipeng Duan; Monica Musso

doi:10.1016/j.jde.2022.07.027

New type of solutions for the nonlinear Schrödinger equation in R^N

Lipeng Duan, Monica Musso

Department of Mathematical Sciences

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

Abstract

We construct a new family of entire solutions for the nonlinear Schrödinger equation {−Δu+V(y)u=u ^p,u>0,inR ^N,u∈H ¹(R ^N), where [Formula presented] and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfying [Formula presented] for some fixed constants V ₀,a,σ>0, and [Formula presented].

Original language	English
Pages (from-to)	479-504
Number of pages	26
Journal	Journal of Differential Equations
Volume	336
Early online date	28 Jul 2022
DOIs	https://doi.org/10.1016/j.jde.2022.07.027
Publication status	Published - 5 Nov 2022

Keywords

Finite Lyapunov-Schmidt reduction
Infinitely many solutions
New solutions
Nonlinear Schrödinger equation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2022.07.027Licence: CC BY

Cite this

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title = "New type of solutions for the nonlinear Schr{\"o}dinger equation in RN",

abstract = "We construct a new family of entire solutions for the nonlinear Schr{\"o}dinger equation {−Δu+V(y)u=u p,u>0,inR N,u∈H 1(R N), where [Formula presented] and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfying [Formula presented] for some fixed constants V 0,a,σ>0, and [Formula presented]. ",

keywords = "Finite Lyapunov-Schmidt reduction, Infinitely many solutions, New solutions, Nonlinear Schr{\"o}dinger equation",

author = "Lipeng Duan and Monica Musso",

note = "Funding Information: L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167 ). M. Musso has been supported by EPSRC research Grant EP/T008458/1 . Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports. Funding Information: L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167). M. Musso has been supported by EPSRC research Grant EP/T008458/1. Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports. Publisher Copyright: {\textcopyright} 2022 The Author(s)",

year = "2022",

month = nov,

day = "5",

doi = "10.1016/j.jde.2022.07.027",

language = "English",

volume = "336",

pages = "479--504",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Elsevier Academic Press Inc",

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TY - JOUR

T1 - New type of solutions for the nonlinear Schrödinger equation in RN

AU - Duan, Lipeng

AU - Musso, Monica

N1 - Funding Information: L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167 ). M. Musso has been supported by EPSRC research Grant EP/T008458/1 . Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports. Funding Information: L. Duan was supported by the China Scholarship Council and NSFC grants (No. 11771167). M. Musso has been supported by EPSRC research Grant EP/T008458/1. Part of this paper was completed during the visit of L. Duan to M. Musso at the University of Bath. L. Duan would like to thank the Department of Mathematical Sciences for its warm hospitality and supports. Publisher Copyright: © 2022 The Author(s)

PY - 2022/11/5

Y1 - 2022/11/5

N2 - We construct a new family of entire solutions for the nonlinear Schrödinger equation {−Δu+V(y)u=u p,u>0,inR N,u∈H 1(R N), where [Formula presented] and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfying [Formula presented] for some fixed constants V 0,a,σ>0, and [Formula presented].

AB - We construct a new family of entire solutions for the nonlinear Schrödinger equation {−Δu+V(y)u=u p,u>0,inR N,u∈H 1(R N), where [Formula presented] and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfying [Formula presented] for some fixed constants V 0,a,σ>0, and [Formula presented].

KW - Finite Lyapunov-Schmidt reduction

KW - Infinitely many solutions

KW - New solutions

KW - Nonlinear Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=85135021226&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2022.07.027

DO - 10.1016/j.jde.2022.07.027

M3 - Article

VL - 336

SP - 479

EP - 504

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -

New type of solutions for the nonlinear Schrödinger equation in R^N

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Concentration phenomena in nonlinear analysis

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New type of solutions for the nonlinear Schrödinger equation in RN

Abstract

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ASJC Scopus subject areas

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Concentration phenomena in nonlinear analysis

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New type of solutions for the nonlinear Schrödinger equation in R^N