一类临界指标椭圆方程解的存在性  

Existence of Solution for an Elliptic Equation Involving Critical Exponents

作　　者：易刚[1] 赵健[1] 

机构地区：[1]商洛学院数学与计算科学系,陕西商洛726000

出　　处：《商洛学院学报》2009年第4期31-33,共3页Journal of Shangluo University

基　　金：商洛学院科研基金项目(08SKY021)

摘　　要：运用变分方法及Hardy不等式讨论了下列椭圆方程:-Δu-μux2=u2*-1+u,x∈Ω其中该方程满足条件u>0,x∈Ω和u=0,x∈Ω,并且μ<μN-22,2*=N2-N2,N≥3,Ω奂RN是包含0的有界光滑区域;并且获得该方程解的存在性。This paper discusses a class special elliptic equation with strong singular item and involving critical Sobolev exponents by Variational method in PDE and Hardy inequality：-△u-μ u/x^2=u^2-1 ＋u,x∈Ωwhich the equation is satisfied u〉0,x ∈Ω and u=0.x∈Ω, and also μ〈μ -N-2/2,2^＊=2N/N-2,N≥3,Ω→∪R^Nis a bound smooth domain which contains zero; Under these conditions we obtain the existence of at least one solution about the equation.

关 键 词：临界椭圆方程 HARDY不等式 奇性项 解的存在性 

分 类 号：O174.54[理学—数学]