含奇异权函数的椭圆方程组边界爆破解的唯一性(英文)  

Uniqueness of boundaryblow-upsolution to an elliptic system with singular weights

作　　者：李晓琴[1] 林先安[2] 郭淑会[2] 

机构地区：[1]甘肃民族师范学院数学系,甘肃合作7470000 [2]湖北工程学院数学与统计学院,湖北孝感432000

出　　处：《浙江大学学报（理学版）》2014年第1期12-17,共6页Journal of Zhejiang University（Science Edition）

基　　金：Supported by National Natural Science Foundation of China(10171082)

摘　　要：通过构造适当的上下解,建立了椭圆方程组Δu=ur(a1um1+b1(x)um+δ1vn),x∈Ω,Δv=vs(a2vp1+b2(x)vp+δ1uq),x∈Ω,u=v=∞,x∈Ω,边界爆破解的边界行为,其中b1(x),b2(x)可能在边界的某一部分有界而在其他部分趋于无穷.进一步,在没有精确的边界行为的情况下,得到了边界爆破解的唯一性.结果表明,为了得到解唯一性,并不需要权函数的精确行为而只需要控制其在边界附近的行为即可.Based on the construction of certain upper and sub-solutions, the boundary behavior of positive boundary blow-up solutions to elliptic systems Au：ur（axu＇nl q-b1 （x）umq-）, xEO, Av=vS（azvpl q-bz（x）vPq-3lUq）, xE , u=v=oo, xE 8l, are obtained, here the singular weight functions bl （x） ,bz （x） are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts. Furthermore, the uniqueness of the boundary blow-up solutions without the exact boundary behavior are also studied. The results show that it is not necessary to impose an exact boundary behavior to the weight functions, but only to control their growth near the boundary for uniqueness.

关 键 词：椭圆方程组 上下解 边界爆破 

分 类 号：O175.25[理学—数学]