Symmetry and regularity of solutions to a system with three-component integral equations

Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a positive constant, p, q and r satisfy some suitable conditions. It is shown that every positive regular solution （u（x...

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Bibliographic Details
Published inScience China. Mathematics Vol. 55; no. 10; pp. 1991 - 2004
Main Authors Qu, ChangZheng, Dou, JingBo
Format Journal Article
LanguageEnglish
Published Heidelberg SP Science China Press 01.10.2012
Subjects
Applications of Mathematics
China
FRN
Integral equations
Integrals
Invariants
Mathematical analysis
Mathematics
Mathematics and Statistics
Planes
Regularity
Symmetry
三分量
压缩映射原理
对称性
径向对称
正规溶液
积分方程
系统
system of integral equations
symmetry
conformal invariance
35B65
regularity
35J45
45G15
Online AccessGet full text
ISSN1674-7283
1869-1862
DOI10.1007/s11425-012-4495-7

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Summary:Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a positive constant, p, q and r satisfy some suitable conditions. It is shown that every positive regular solution （u（x）, v（x）, w（x）） is radially symmetric and monotonic about some point by developing the moving plane method in an integral form. In addition, the regularity of the solutions is also proved by the contraction mapping principle. The conformal invariant property of the system is also investigated.
Bibliography:system of integral equations, symmetry, regularity, conformal invariance
Consider the system with three-component integral equations{u（x） ：fRn│x - y│α-nw（y）^v（y）^qdy,v（x） =fRn│x-y│^α-nu（y）^pw（y）^rdy, w（x） =fRn│x - y│α-nv（y）qu（y）Pdy,where 0 〈 a 〈 n, n is a positive constant, p, q and r satisfy some suitable conditions. It is shown that every positive regular solution （u（x）, v（x）, w（x）） is radially symmetric and monotonic about some point by developing the moving plane method in an integral form. In addition, the regularity of the solutions is also proved by the contraction mapping principle. The conformal invariant property of the system is also investigated.
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ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1674-7283
1869-1862
DOI:10.1007/s11425-012-4495-7