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

Yuxia Guo, Monica Musso, Shuangjie Peng, Shusen Yan

Research output: Contribution to journalArticle

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.

Original languageEnglish
Article number108553
JournalJournal of Functional Analysis
Volume279
Issue number6
Early online date9 Apr 2020
DOIs
Publication statusE-pub ahead of print - 9 Apr 2020

Keywords

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

ASJC Scopus subject areas

  • Analysis

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