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

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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

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",

year = "2018",

month = jun,

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doi = "10.1016/j.jde.2018.01.046",

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AU - Musso, Monica

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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M3 - Article

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SN - 0022-0396

VL - 264

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EP - 6709

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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