Non-degeneracy and existence of new solutions for the Schrödinger equations

Yuxia Guo; Monica Musso; Shuangjie Peng; Shusen Yan

doi:10.1016/j.jde.2022.04.016

Non-degeneracy and existence of new solutions for the Schrödinger equations

Yuxia Guo, Monica Musso, Shuangjie Peng, Shusen Yan

Department of Mathematical Sciences

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

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Abstract

We consider the following nonlinear problem −Δu+V(|y|)u=u^p,u>0inR^N,u∈H¹(R^N), where V(r) is a positive function, 1<p<[Formula presented]. We show that the multi-bump solutions constructed in [27] are non-degenerate in a suitable symmetric space. We also use this non-degenerate result to construct new solutions for (0.1).

Original language	English
Pages (from-to)	254-279
Number of pages	26
Journal	Journal of Differential Equations
Volume	326
Early online date	22 Apr 2022
DOIs	https://doi.org/10.1016/j.jde.2022.04.016
Publication status	Published - 25 Jul 2022

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2022.04.016

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title = "Non-degeneracy and existence of new solutions for the Schr{\"o}dinger equations",

abstract = "We consider the following nonlinear problem −Δu+V(|y|)u=up,u>0inRN,u∈H1(RN), where V(r) is a positive function, 1",

author = "Yuxia Guo and Monica Musso and Shuangjie Peng and Shusen Yan",

note = "Funding Information: Y. Guo was supported by NNSF of China (No. 12031015 ). M. Musso was supported by EPSRC research Grant EP/T008458/1 . S. Peng was supported by NNSF of China (No. 11831009 ). S. Yan was supported by NNSF of China (No. 12171184 ). ",

year = "2022",

month = jul,

day = "25",

doi = "10.1016/j.jde.2022.04.016",

language = "English",

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journal = "Journal of Differential Equations",

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T1 - Non-degeneracy and existence of new solutions for the Schrödinger equations

AU - Guo, Yuxia

AU - Musso, Monica

AU - Peng, Shuangjie

AU - Yan, Shusen

N1 - Funding Information: Y. Guo was supported by NNSF of China (No. 12031015 ). M. Musso was supported by EPSRC research Grant EP/T008458/1 . S. Peng was supported by NNSF of China (No. 11831009 ). S. Yan was supported by NNSF of China (No. 12171184 ).

PY - 2022/7/25

Y1 - 2022/7/25

N2 - We consider the following nonlinear problem −Δu+V(|y|)u=up,u>0inRN,u∈H1(RN), where V(r) is a positive function, 1

AB - We consider the following nonlinear problem −Δu+V(|y|)u=up,u>0inRN,u∈H1(RN), where V(r) is a positive function, 1

UR - http://www.scopus.com/inward/record.url?scp=85130882318&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2022.04.016

DO - 10.1016/j.jde.2022.04.016

M3 - Article

AN - SCOPUS:85130882318

SN - 0022-0396

VL - 326

SP - 254

EP - 279

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Non-degeneracy and existence of new solutions for the Schrödinger equations

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Concentration phenomena in nonlinear analysis

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Non-degeneracy and existence of new solutions for the Schrödinger equations

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Concentration phenomena in nonlinear analysis

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