带临界Sobolev指标椭圆方程解的存在性  

Existence of Solution for an Elliptic Equation Involving Critical Sobolev Exponents

作　　者：张毅[1] 

机构地区：[1]长江大学信息与数学学院,湖北荆州434023

出　　处：《太原师范学院学报（自然科学版）》2009年第2期38-40,共3页Journal of Taiyuan Normal University:Natural Science Edition

摘　　要：文章运用变分方法及Hardy不等式讨论了椭圆方程:-Δu-μux2=u2*-1+λu,x∈Ω,其中该方程满足条件u>0,x∈Ω和u=0,x∈Ω,并且μ<μ=[N-2/2]2,2*=2N/N-2,N≥3,ΩRN是包含0的有界光滑区域;并且对任一λ>0获得该方程解的存在性.[Abstract] The article discusses a class special elliptic equation with strong singular item and involving critical Sobolev exponents by variational method in PDE and Hardy inequality： , -Δu-μux2=u2＊-1＋λu,x∈Ω which the equation is satisfied u〉0,x∈Ω and u=0,x∈Ω ,and μ〈μ=[N-2/2]2,2＊=2N/N-2,N≥3,ΩRN is a bound smooth domain which contains zero ; Under these conditions we obtain the existence of at least one solution about the equation for every λ〉0.

关 键 词：临界椭圆方程 HARDY不等式 奇性项 解的存在性 

分 类 号：O174.45[理学—数学]