High energy sign-changing solutions for Coron's problem

Shengbing Deng, Monica Musso

Research output: Contribution to journalArticle

Abstract

We study the existence of sign changing solutions to the following problem {Δu+|u|p−1u=0inΩε;u=0on∂Ωε, where [Formula presented] is the critical Sobolev exponent and Ωε is a bounded smooth domain in Rn, n≥3, of the form Ωε=Ω\B(0,ε). Here Ω is a smooth bounded domain containing the origin 0 and B(0,ε) denotes the ball centered at the origin with radius ε>0. We construct a new type of sign-changing solutions with high energy to problem (0.1), when the parameter ε is small enough.

Original languageEnglish
Pages (from-to)916-962
Number of pages47
JournalJournal of Differential Equations
Volume271
Early online date24 Sep 2020
DOIs
Publication statusE-pub ahead of print - 24 Sep 2020

Keywords

  • Concentration phenomenon of solutions
  • Coron's problem
  • Critical Sobolev exponent
  • Sign-changing solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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