摘要
当N 4时,Capozzi A(1985),Ambrosetti A(1986)给出了具临界指数2*的椭圆型方程-Δku+|u|2*-2u,inΩRN;u=0,onΩ(*)非平凡解的存在性结论,其中λk是算子-Δ的第k个特征值。然而N=3是问题(*)的临界维数,在适当添加一个次临界扰动项后,利用P.L.Lions集中紧性原理获得了一对非平凡解的存在性结论。
It is well known that Capozzi A( 1985 ) and Ambrosetti A(1986) have got existence theorems of the fol- lowing elliptic equation with critical Sobolev exponent if N ≥ 4,△Ku+|u|^2*-2u,inΩ∈R^N;u=O,on ЭΩ
where λk is the kth eigen - value of - △. However,N = 3 is the critical dimension of the problem( * ). Adding a subcritical perturbation,the authors have given existence theorems by ways of the concentration - compactness principle of P. L. Lions.
出处
《南昌大学学报(理科版)》
CAS
北大核心
2008年第1期28-33,37,共7页
Journal of Nanchang University(Natural Science)
基金
国家自然科学基金资助项目(10571150)
关键词
DIRICHLET问题
临界指数
集中紧性原理
dirichlet problem
critical sobolev exponent
concentration - cmpactness principle