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

Southwest University

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

3 Citations (SciVal)

66 Downloads (Pure)

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 Sept 2020
DOIs	https://doi.org/10.1016/j.jde.2020.09.021
Publication status	Published - 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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10.1016/j.jde.2020.09.021

sign change-coron-final-revised2020Accepted author manuscript, 241 KBLicence: CC BY-NC-ND

Cite this

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title = "High energy sign-changing solutions for Coron's problem",

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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AU - Musso, Monica

PY - 2021/1/15

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N2 - 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.

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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DO - 10.1016/j.jde.2020.09.021

M3 - Article

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SN - 0022-0396

VL - 271

SP - 916

EP - 962

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

High energy sign-changing solutions for Coron's problem

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Concentration phenomena in nonlinear analysis

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High energy sign-changing solutions for Coron's problem

Abstract

Funding

Keywords

ASJC Scopus subject areas

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Fingerprint

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Concentration phenomena in nonlinear analysis

Cite this