Multispike solutions for the Brezis–Nirenberg problem in dimension three

Monica Musso; Dora Salazar

doi:10.1016/j.jde.2018.01.046

Multispike solutions for the Brezis–Nirenberg problem in dimension three

Monica Musso
, Dora Salazar

Department of Mathematical Sciences

Pontificia Universidad Católica de Chile
Universidad Nacional de Colombia

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

19 Citations (SciVal)

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Abstract

We consider the problem Δu+λu+u⁵=0, u>0, in a smooth bounded domain Ω in R³, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ₀, which we characterize in terms of the Green function of −Δ−λ.

Original language	English
Pages (from-to)	6663-6709
Number of pages	47
Journal	Journal of Differential Equations
Volume	264
Issue number	11
Early online date	6 Feb 2018
DOIs	https://doi.org/10.1016/j.jde.2018.01.046
Publication status	Published - 5 Jun 2018

Funding

The research of M. Musso has been partly supported by FONDECYT Grant 1120151 and Millennium Nucleus Center for Analysis of PDE, NC130017. D. Salazar was partially funded by grant Hermes 35454 from Universidad Nacional de Colombia sede Medellín and Millennium Nucleus Center for Analysis of PDE, NC130017.

ASJC Scopus subject areas

Analysis

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10.1016/j.jde.2018.01.046

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title = "Multispike solutions for the Brezis–Nirenberg problem in dimension three",

abstract = "We consider the problem Δu+λu+u5=0, u>0, in a smooth bounded domain Ω in R3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ0, which we characterize in terms of the Green function of −Δ−λ.",

author = "Monica Musso and Dora Salazar",

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AU - Salazar, Dora

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N2 - We consider the problem Δu+λu+u5=0, u>0, in a smooth bounded domain Ω in R3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ0, which we characterize in terms of the Green function of −Δ−λ.

AB - We consider the problem Δu+λu+u5=0, u>0, in a smooth bounded domain Ω in R3, under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ0, which we characterize in terms of the Green function of −Δ−λ.

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 11

ER -

Multispike solutions for the Brezis–Nirenberg problem in dimension three

Abstract

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