Isolated singularities of positive solutions for Choquard equations in sublinear case

Huyuan Chen; Feng Zhou

doi:10.1142/S0219199717500407

Isolated singularities of positive solutions for Choquard equations in sublinear case

Huyuan Chen
, Feng Zhou

数学科学学院

Jiangxi Normal University

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case q (0, 1) (x) = 0, where p > 0,N ≥ 3,α (0,N) and Iα[up](x) =N up(y) |x-y|N-αdy is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent (p,q). Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.

源语言	英语
文章编号	1750040
期刊	Communications in Contemporary Mathematics
卷	20
期	4
DOI	https://doi.org/10.1142/S0219199717500407
出版状态	已出版 - 1 6月 2018

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abstract = "Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case q (0, 1) (x) = 0, where p > 0,N ≥ 3,α (0,N) and Iα[up](x) =N up(y) |x-y|N-αdy is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent (p,q). Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.",

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T1 - Isolated singularities of positive solutions for Choquard equations in sublinear case

AU - Chen, Huyuan

AU - Zhou, Feng

PY - 2018/6/1

Y1 - 2018/6/1

N2 - Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case q (0, 1) (x) = 0, where p > 0,N ≥ 3,α (0,N) and Iα[up](x) =N up(y) |x-y|N-αdy is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent (p,q). Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.

AB - Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case q (0, 1) (x) = 0, where p > 0,N ≥ 3,α (0,N) and Iα[up](x) =N up(y) |x-y|N-αdy is the Riesz potential, which appears as a nonlocal term in the equation. We investigate the nonexistence and existence of isolated singular solutions of Choquard equation under different range of the pair of exponent (p,q). Furthermore, we obtain qualitative properties for the minimal singular solutions of the equation.

KW - Choquard equation

KW - Classification of singularity

KW - Dirac mass

KW - polynomial decay

KW - sublinear case

UR - https://www.scopus.com/pages/publications/85019769870

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DO - 10.1142/S0219199717500407

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SN - 0219-1997

VL - 20

JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 4

M1 - 1750040

ER -

Isolated singularities of positive solutions for Choquard equations in sublinear case

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