Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

Zongming Guo; Juncheng Wei; Feng Zhou

doi:10.1016/j.jde.2017.03.019

Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

Zongming Guo
, Juncheng Wei
, Feng Zhou^*

^*此作品的通讯作者

数学科学学院

Henan Normal University
University of British Columbia

科研成果: 期刊稿件 › 文章 › 同行评审

29 引用（Scopus）

摘要

Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Δ²u=u^pin Ω,u=Δu=0on ∂Ω where Ω is a smooth open set of Rⁿ with n≥5.

源语言	英语
页（从-至）	1188-1224
页数	37
期刊	Journal of Differential Equations
卷	263
期	2
DOI	https://doi.org/10.1016/j.jde.2017.03.019
出版状态	已出版 - 15 7月 2017

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10.1016/j.jde.2017.03.019

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title = "Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation",

abstract = "Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Δ2u=upin Ω,u=Δu=0on ∂Ω where Ω is a smooth open set of Rn with n≥5.",

keywords = "Biharmonic equations, Radial singular entire solutions, Solutions with prescribed isolated singularities",

author = "Zongming Guo and Juncheng Wei and Feng Zhou",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = jul,

day = "15",

doi = "10.1016/j.jde.2017.03.019",

language = "英语",

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T1 - Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

AU - Guo, Zongming

AU - Wei, Juncheng

AU - Zhou, Feng

PY - 2017/7/15

Y1 - 2017/7/15

N2 - Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Δ2u=upin Ω,u=Δu=0on ∂Ω where Ω is a smooth open set of Rn with n≥5.

AB - Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Δ2u=upin Ω,u=Δu=0on ∂Ω where Ω is a smooth open set of Rn with n≥5.

KW - Biharmonic equations

KW - Radial singular entire solutions

KW - Solutions with prescribed isolated singularities

UR - https://www.scopus.com/pages/publications/85016552754

U2 - 10.1016/j.jde.2017.03.019

DO - 10.1016/j.jde.2017.03.019

M3 - 文章

AN - SCOPUS:85016552754

SN - 0022-0396

VL - 263

SP - 1188

EP - 1224

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Singular radial entire solutions and weak solutions with prescribed singular set for a biharmonic equation

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