摘要
利用积分形式的移动平面法,给出n维上半空间R_+~n积分方程组{u(x)rn+(1|x-y|n-a-1|x*-y|n-a)(γ1up1(y)+u1vp2(y)+βup3(y)vp4(y)dyv(x)=rn+(1|x-y|n-a-|x*-y|n-a)(γ1uq1(y)+u2vq2(y)+β2uq3(y)vq4(y)dy}解的单调性和旋转对称性,其中0<α<n,λ_i,μ_i,β_i≥0(i=1,2)是非负常数,pi,qi(i=1,2,3,4)满足适当的假设,x~*=(x_1,x_2,…,x_(n-1),-x_n)是点x关于超平面x_n=0的反射点.本文的结果推广了n维欧氏空间R^n中的结果.
The monotonicity and rotational symmetry for solutions to the following integral system in the n-dimensional upper half Euclidean space R_+~n= {x =(x_1,x_2,…,x_n) ∈R^n | x_n > 0},{u(x)rn+(1|x-y|n-a-1|x*-y|n-a)(γ1up1(y)+u1vp2(y)+βup3(y)vp4(y)dyv(x)=rn+(1|x-y|n-a-|x*-y|n-a)(γ1uq1(y)+u2vq2(y)+β2uq3(y)vq4(y)dy} are given by moving plane method in integral forms,where 0 < a < n,λ_i,μ_i,β_i > 0 i = 1,2)are nonnegative constants,p_i and q_i(i = 1,2,3,4) satisfy some suitable assumptions,and x~* =(x_1,x_2,…,x_(n-1,-x_n)) is the reflection of the point x about the hyperplane x_n= 0.Results in this paper generalize results on the n-dimensional Euclidean space R^n.
出处
《数学进展》
CSCD
北大核心
2014年第6期942-950,共9页
Advances in Mathematics（China）
基金
Supported by Chinese National Science Fund for Distinguished Young Scholars(No.11101319,No.11201081,No.11202035)
the Foundation of Shaanxi Statistical Research Center(No.13JD04)
the Foundation of Shaanxi Province Education Department(No.14JK1276)
关键词
积分方程组
积分形式的移动平面法
旋转对称
上半空间
system of integral equations
moving plane method in integral forms
rotational symmetry
upper half space
