High energy sign-changing solutions for Coron's problem

Shengbing Deng; Monica Musso

doi:10.1016/j.jde.2020.09.021

High energy sign-changing solutions for Coron's problem

Shengbing Deng, Monica Musso

Department of Mathematical Sciences

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

Abstract

We study the existence of sign changing solutions to the following problem {Δu+|u|^p−1u=0inΩ_ε;u=0on∂Ω_ε, where [Formula presented] is the critical Sobolev exponent and Ω_ε is a bounded smooth domain in Rⁿ, n≥3, of the form Ω_ε=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 language	English
Pages (from-to)	916-962
Number of pages	47
Journal	Journal of Differential Equations
Volume	271
Early online date	24 Sep 2020
DOIs	https://doi.org/10.1016/j.jde.2020.09.021
Publication status	Published - 15 Jan 2021

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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10.1016/j.jde.2020.09.021

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sign change-coron-final-revised2020
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1 Active

Concentration phenomena in nonlinear analysis
Musso, M.
Engineering and Physical Sciences Research Council
27/04/20 → 26/04/23
Project: Research council

Cite this

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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.",

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author = "Shengbing Deng and Monica Musso",

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AB - 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.

KW - Concentration phenomenon of solutions

KW - Coron's problem

KW - Critical Sobolev exponent

KW - Sign-changing solutions

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EP - 962

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -

High energy sign-changing solutions for Coron's problem

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Embargoed Document

Concentration phenomena in nonlinear analysis

Cite this