Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

Yuxia Guo; Monica Musso; Shuangjie Peng; Shusen Yan

doi:10.1016/j.jfa.2020.108553

Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

Yuxia Guo, Monica Musso, Shuangjie Peng, Shusen Yan

Department of Mathematical Sciences

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44 Citations (SciVal)

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Abstract

We consider the following prescribed scalar curvature equations in R^N −Δu=K(|y|)u^{2^⁎−1},u>0inR^N,u∈D^1,2(R^N), where K(r) is a positive function, [Formula presented]. We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in [26] by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.

Original language	English
Article number	108553
Journal	Journal of Functional Analysis
Volume	279
Issue number	6
Early online date	9 Apr 2020
DOIs	https://doi.org/10.1016/j.jfa.2020.108553
Publication status	Published - 1 Oct 2020

Funding

Y. Guo was supported by NNSF of China (No. 11771235 ). M. Musso was supported by EPSRC research grant EP/T008458/1 . S. Peng was supported by NNSF of China (No. 11571130 , No. 11831009 ). S. Yan was supported by NNSF of China (No. 11629101 ).

Keywords

Bubbling analysis
Critical Sobolev exponent
Non-degeneracy of entire solutions
Pohozaev identity

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2020.108553

gmpy final for jfa.PDFAccepted author manuscript, 157 KBLicence: CC BY-NC-ND

Cite this

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title = "Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications",

abstract = "We consider the following prescribed scalar curvature equations in RN −Δu=K(|y|)u2⁎−1,u>0inRN,u∈D1,2(RN), where K(r) is a positive function, [Formula presented]. We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in [26] by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.",

keywords = "Bubbling analysis, Critical Sobolev exponent, Non-degeneracy of entire solutions, Pohozaev identity",

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

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doi = "10.1016/j.jfa.2020.108553",

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T1 - Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

AU - Guo, Yuxia

AU - Musso, Monica

AU - Peng, Shuangjie

AU - Yan, Shusen

PY - 2020/10/1

Y1 - 2020/10/1

N2 - We consider the following prescribed scalar curvature equations in RN −Δu=K(|y|)u2⁎−1,u>0inRN,u∈D1,2(RN), where K(r) is a positive function, [Formula presented]. We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in [26] by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.

AB - We consider the following prescribed scalar curvature equations in RN −Δu=K(|y|)u2⁎−1,u>0inRN,u∈D1,2(RN), where K(r) is a positive function, [Formula presented]. We first prove a non-degeneracy result for the positive multi-bubbling solutions constructed in [26] by using the local Pohozaev identities. Then we use this non-degeneracy result to glue together bubbles with different concentration rate to obtain new solutions.

KW - Bubbling analysis

KW - Critical Sobolev exponent

KW - Non-degeneracy of entire solutions

KW - Pohozaev identity

UR - https://www.scopus.com/pages/publications/85084343282

U2 - 10.1016/j.jfa.2020.108553

DO - 10.1016/j.jfa.2020.108553

M3 - Article

AN - SCOPUS:85084343282

SN - 0022-1236

VL - 279

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 6

M1 - 108553

ER -

Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

Abstract

Funding

Keywords

ASJC Scopus subject areas

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Concentration phenomena in nonlinear analysis

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Non-degeneracy of multi-bubbling solutions for the prescribed scalar curvature equations and applications

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

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Concentration phenomena in nonlinear analysis

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