收稿日期: 2009-09-25
修回日期: 2009-12-14
网络出版日期: 2010-05-15
基金资助
Supported by the National Natural Science Foundation of China (10802061) and Natural Science Basic Research Plan in Shaanxi Province of China(SJ08F27)
Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight
Received date: 2009-09-25
Revised date: 2009-12-14
Online published: 2010-05-15
Supported by
Supported by the National Natural Science Foundation of China (10802061) and Natural Science Basic Research Plan in Shaanxi Province of China(SJ08F27)
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 - Δ u-μ u |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 R <em>N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 上有界正函数.
关键词： Hardy-Sobolev临界指数; 半线性椭圆方程; 环绕定理; 非平凡解
窦井波 . 带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解[J]. 中国科学院大学学报, 2010 , 27(3) : 306 -313 . DOI: 10.7523/j.issn.2095-6134.2010.3.002
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 - Δ u-μ u |x|2 =λu+K(x) |u|2*(s)-2u |x|s , x∈Ω; u=0, x∈Ω, where Ω is an open bounded domain of R <em>N with smooth boundary Ω and 0∈Ω, N≥5, 0<s<2,0≤μ< N-2 2 2, λ>0, and K (x) is a bounded positive function on Ω.
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