High energy sign-changing solutions for Coron's problem

Shengbing Deng, Monica Musso

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)
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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 Sept 2020
DOIs
Publication statusPublished - 15 Jan 2021

Funding

The first author has been supported by NSFC No. 11971392, Natural Science Foundation of Chongqing, China cstc2019jcyjjqX0022 and Fundamental Research Funds for the Central Universities XDJK2019TY001. The second author has been supported by EPSRC research Grant EP/T008458/1.

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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