Properties of solutions to semilinear elliptic problem with Hardy potential

Jann Long Chern; Masato Hashizume; Gyeongha Hwang

doi:10.1016/j.jde.2020.01.009

Properties of solutions to semilinear elliptic problem with Hardy potential

Jann Long Chern, Masato Hashizume, Gyeongha Hwang^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We consider the following nonlinear Neumann problem [Formula presented] where [Formula presented], 0<s<2, [Formula presented] and B_R is the ball centered at the origin with radius R. Firstly, we establish the existence of infinitely many positive radial solutions which are singular at the origin. Secondly, we investigate the existence and regularity of a least-energy solution. Lastly, we study the symmetric properties of a regular least-energy solution.

Original language	English
Pages (from-to)	1432-1464
Number of pages	33
Journal	Journal of Differential Equations
Volume	269
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2020.01.009
Publication status	Published - 2020 Jul 5
Externally published	Yes

Keywords

Existence
Hardy potential
Neumann problem
Semilinear elliptic equation
Symmetric properties

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2020.01.009

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title = "Properties of solutions to semilinear elliptic problem with Hardy potential",

abstract = "We consider the following nonlinear Neumann problem [Formula presented] where [Formula presented], 0R is the ball centered at the origin with radius R. Firstly, we establish the existence of infinitely many positive radial solutions which are singular at the origin. Secondly, we investigate the existence and regularity of a least-energy solution. Lastly, we study the symmetric properties of a regular least-energy solution.",

keywords = "Existence, Hardy potential, Neumann problem, Semilinear elliptic equation, Symmetric properties",

author = "Chern, {Jann Long} and Masato Hashizume and Gyeongha Hwang",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = jul,

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doi = "10.1016/j.jde.2020.01.009",

language = "English",

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T1 - Properties of solutions to semilinear elliptic problem with Hardy potential

AU - Chern, Jann Long

AU - Hashizume, Masato

AU - Hwang, Gyeongha

PY - 2020/7/5

Y1 - 2020/7/5

N2 - We consider the following nonlinear Neumann problem [Formula presented] where [Formula presented], 0R is the ball centered at the origin with radius R. Firstly, we establish the existence of infinitely many positive radial solutions which are singular at the origin. Secondly, we investigate the existence and regularity of a least-energy solution. Lastly, we study the symmetric properties of a regular least-energy solution.

AB - We consider the following nonlinear Neumann problem [Formula presented] where [Formula presented], 0R is the ball centered at the origin with radius R. Firstly, we establish the existence of infinitely many positive radial solutions which are singular at the origin. Secondly, we investigate the existence and regularity of a least-energy solution. Lastly, we study the symmetric properties of a regular least-energy solution.

KW - Existence

KW - Hardy potential

KW - Neumann problem

KW - Semilinear elliptic equation

KW - Symmetric properties

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DO - 10.1016/j.jde.2020.01.009

M3 - Article

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SN - 0022-0396

VL - 269

SP - 1432

EP - 1464

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Properties of solutions to semilinear elliptic problem with Hardy potential

Abstract

Keywords

ASJC Scopus subject areas

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