具Dirichlet边界条件积分方程组的对称性研究  

Research on the Symmetry of Integral Equations with Dirichlet Boundary Conditions

作　　者：张曼玉 张春华 ZHANG Man-yu;ZHANG Chun-hua(School of Mathematics and Information Science,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063

出　　处：《南昌航空大学学报（自然科学版）》2023年第4期46-51,共6页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：江西省主要学科学术和技术带头人培养计划—青年人才(2021BCJ23027);江西省双千计划—青年项目(jxsq2023201115)。

摘　　要：考虑如下具Dirichlet边值条件的积分方程组:■其中,R_(+)^(n)为n维欧式空间的上半部分,Gi(x,y)是R_(+)^(n)中满足Dirichlet边值条件的格林函数,fi(u)(i=1,2,…,m)是实值函数。本文假设积分方程组在R_(+)^(n)上存在满足一定可积性的正解ui,利用积分形式的移动平面法,证明了正解ui关于某条轴径向对称。In this paper,we consider the following integral equations with Dirichlet boundary conditions:■where R4 is the n-dimensional upper half Euc lidean space,G(x,y)is the Green's function with Dirichlet boundary conditions in R_(+)^(n)f(u)(i=1,2,…m)is real-valued function.In this paper,assuming that the system of integral equations has a positive solution ui that satisfies certain integrability in R_(+)^(n)and using the method of moving planes in integral forms,we prove that the positive solutions uli is rotationally sy mmetric about some line.

关 键 词：Dirichlet边值条件 积分方程 径向对称 移动平面法 

分 类 号：O175.2[理学—数学] O175.6[理学—基础数学]