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

作　　者：QU ChangZheng DOU JingBo 

机构地区：[1]Department of Mathematics,Ningbo University,Ningbo 315211,China [2]School of Statistics,Xi'an University of Finance and Economics,Xi'an 710100,China

出　　处：《Science China Mathematics》2012年第10期1991-2004,共14页中国科学：数学（英文版）

基　　金：supported by National National Science Foundation of China for Distinguished Young Scholars (Grant No. 10925104);National National Science Foundation of China (Grant No.11101319);the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549)

摘　　要：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.Consider the system with three-component integral equations u(x) = Rn |x y|α nw(y)rv(y)q dy,v(x) = Rn |x y|α nu(y)pw(y)rdy,w(x) = Rn |x y|α nv(y)q u(y)pdy,where 0 < α < 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.

关 键 词：system of integral equations SYMMETRY REGULARITY conformal invariance 

分 类 号：O175.5[理学—数学] P631.4[理学—基础数学]