Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes

Wei Dai; Yanqin Fang; Guolin Qin

doi:10.1016/j.jde.2018.04.026

Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes

Wei Dai^*
, Yanqin Fang
, Guolin Qin

^*Corresponding author for this work

School of Mathematical Sciences

Hunan University
University of Wollongong
Beihang University

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

51 Scopus citations

Abstract

In this paper, we are concerned with the fractional order static Hartree equations with critical nonlocal nonlinearity. We prove that the positive solutions are radially symmetric about some point in R^d and must assume the certain explicit forms. The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving plane method for fractional Laplacians in [6]. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Decay at infinity and Narrow region principle (Theorem 2.1 and 2.6).

Original language	English
Pages (from-to)	2044-2063
Number of pages	20
Journal	Journal of Differential Equations
Volume	265
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2018.04.026
State	Published - 5 Sep 2018

Keywords

Direct methods of moving planes
Fractional Laplacians
Hartree type nonlinearity
Positive solutions
Radial symmetry
Uniqueness

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10.1016/j.jde.2018.04.026

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title = "Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes",

abstract = "In this paper, we are concerned with the fractional order static Hartree equations with critical nonlocal nonlinearity. We prove that the positive solutions are radially symmetric about some point in Rd and must assume the certain explicit forms. The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving plane method for fractional Laplacians in [6]. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Decay at infinity and Narrow region principle (Theorem 2.1 and 2.6).",

keywords = "Direct methods of moving planes, Fractional Laplacians, Hartree type nonlinearity, Positive solutions, Radial symmetry, Uniqueness",

author = "Wei Dai and Yanqin Fang and Guolin Qin",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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doi = "10.1016/j.jde.2018.04.026",

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T1 - Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes

AU - Dai, Wei

AU - Fang, Yanqin

AU - Qin, Guolin

PY - 2018/9/5

Y1 - 2018/9/5

N2 - In this paper, we are concerned with the fractional order static Hartree equations with critical nonlocal nonlinearity. We prove that the positive solutions are radially symmetric about some point in Rd and must assume the certain explicit forms. The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving plane method for fractional Laplacians in [6]. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Decay at infinity and Narrow region principle (Theorem 2.1 and 2.6).

AB - In this paper, we are concerned with the fractional order static Hartree equations with critical nonlocal nonlinearity. We prove that the positive solutions are radially symmetric about some point in Rd and must assume the certain explicit forms. The arguments used in our proof is a variant (for nonlocal nonlinearity) of the direct moving plane method for fractional Laplacians in [6]. The main ingredients are the variants (for nonlocal nonlinearity) of the maximum principles, i.e., Decay at infinity and Narrow region principle (Theorem 2.1 and 2.6).

KW - Direct methods of moving planes

KW - Fractional Laplacians

KW - Hartree type nonlinearity

KW - Positive solutions

KW - Radial symmetry

KW - Uniqueness

UR - https://www.scopus.com/pages/publications/85045440057

U2 - 10.1016/j.jde.2018.04.026

DO - 10.1016/j.jde.2018.04.026

M3 - 文章

AN - SCOPUS:85045440057

SN - 0022-0396

VL - 265

SP - 2044

EP - 2063

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 5

ER -

Classification of positive solutions to fractional order Hartree equations via a direct method of moving planes

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Keywords

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