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^*

^*Corresponding author for this work

School of Mathematical Sciences

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

27 Scopus citations

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=u^pin Ω,u=Δu=0on ∂Ω where Ω is a smooth open set of Rⁿ with n≥5.

Original language	English
Pages (from-to)	1188-1224
Number of pages	37
Journal	Journal of Differential Equations
Volume	263
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2017.03.019
State	Published - 15 Jul 2017

Keywords

Biharmonic equations
Radial singular entire solutions
Solutions with prescribed isolated singularities

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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",

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

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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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Keywords

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