Symmetry and nonexistence of positive solutions to an integral system with weighted functions

作     者：DOU JingBo QU ChangZheng HAN YaZhou 

作者机构：Center for Nonlinear StudiesNorthwest UniversityXi'an 710069China School of StatisticsXi'an University of Finance and EconomicsXi'an 710100China Department of MathematicsCollege of ScienceChina Jiliang UniversityHangzhou 310018China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2011年第54卷第4期

页      面：753-768页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0802[工学-机械工程] 0835[工学-软件工程] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

基　　金：supported by Chinese National Science Fund for Distinguished Young Scholars (Grant No.10925104) National Natural Science Foundation of China (Grant No.11001221) the Foundation of Shaanxi Province Education Department (Grant No. 2010JK549) the Foundation of Xi’an Statistical Research Institute (Grant No.10JD04) 

主　　题：Hardy-Littlewood-Sobolev inequality system of integral equations symmetry regularity conformally invariant property 

摘      要：Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 α n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) p1q ∞1,Q(x) and K(x) satisfy some suitable *** is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral ***,regularity of the solution is ***,the nonexistence of positive solutions to the system in the case 0 p1q (n+α)/(n-α) is also discussed.