摘要
通过上下解方法和极大值原理,证明了当ε很小时,椭圆系统-Δu=F/u(x,u,v)+εg(x)x∈Ω-Δv=F/v(x,u,v)+εh(x)x∈Ωu>0,v>0x∈Ωu=v=0x∈Ω的极小正解的存在性,其中Ω是RN上的有界光滑区域;F∈C1(Ω×(R+)2,R+);g,h∈C1(Ω);ε是正参数.此外,也证明了当ε很大时该系统无解.
With the sub-supersolution method and the maximum principle,.the existence of a minimal positive solution is proved for the following system -△u=δF/δu(x,u,v)+εg(x),-△v=δF/δv(x,u,v)+εh(x)inΩ;u,v〉0 in Ω;and u=v=0 on δΩ,with ε sufficiently small, where Ω is a bounded smooth domain in R^N ;F∈C^1(-↑Ω×(R^+)^2,R^+);g,h∈C^1(-↑Ω);and e is a positive parameter. In addition, it is proved that the problem has no solution for ε large enough.
出处
《西南大学学报(自然科学版)》
CAS
CSCD
北大核心
2008年第2期5-9,共5页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金资助项目(10771173)
国家数学天元基金资助项目(10726004)
关键词
椭圆系统
上下解方法
极大值原理
正解
elliptic system
sub-supersolution method
the maximum principle
positive solution