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

9 Citations (SciVal)

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

Bibliographical 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 ).

Funding

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 ).

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2022.04.016

Cite this

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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 ). ",

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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

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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

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

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Concentration phenomena in nonlinear analysis

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

Abstract

Bibliographical note

Funding

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Concentration phenomena in nonlinear analysis

Cite this