带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解(英文)  

Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight

作　　者：窦井波[1] 

机构地区：[1]西安财经学院统计学院,西安710100

出　　处：《中国科学院研究生院学报》2010年第3期306-313,共8页Journal of the Graduate School of the Chinese Academy of Sciences

基　　金：Supported by the National Natural Science Foundation of China (10802061);Natural Science Basic Research Plan in Shaanxi Province of China(SJ08F27)

摘　　要：借助环绕定理和非线性分析技巧,研究如下一类带Hardy-Sobolev临界指数和权函数的半线性椭圆方程{-Δu-μu/(|x|~2)=λu+K(x)(|u|~2^(s)-2u)/(|x|~s),x∈Ω;u=0,x∈Ω,,解的存在性,其中Ω是RN具有光滑边界的有界开区域,0∈Ω,N≥5,0≤s≤2,0≤μ≤〔(N-2)/2〕~2,λ>0,K(x)是Ω上有界正函数.Using linking theorem and analytic technique, we discuss the existence of nontrivial solutions for the following semilinear elliptic problem with Hardy-Sobolev critical exponents and weights {-Δu-μu/（｜x｜~2）=λu＋K（x）（｜u｜~2^（s）-2 u）/（｜x｜~s）,x∈Ω;u=0,x∈Ω,where Ω is an open bounded domain of R^N with smooth boundary Ω and 0∈Ω, N≥5, 0s2,0≤μ〔（N-2）/2〕~2, λ0, and K （x） is a bounded positive function on Ω.

关 键 词：HARDY-SOBOLEV临界指数 半线性椭圆方程 环绕定理 非平凡解 

分 类 号：O175.25[理学—数学]