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

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

4 Citations (SciVal)

5 Downloads (Pure)

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

Keywords

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

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2020.108553

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

Cite this

@article{0121e912105345b996d278543c01efa9,

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",

year = "2020",

month = oct,

day = "1",

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

language = "English",

volume = "279",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier Academic Press Inc",

number = "6",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=85084343282&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2020.108553

DO - 10.1016/j.jfa.2020.108553

M3 - Article

AN - SCOPUS:85084343282

VL - 279

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 6

M1 - 108553

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Concentration phenomena in nonlinear analysis

Cite this

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Concentration phenomena in nonlinear analysis

Cite this