带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解

doi:10.7523/j.issn.2095-6134.2010.3.002

中国科学院大学学报 ›› 2010, Vol. 27 ›› Issue (3): 306-313.DOI: 10.7523/j.issn.2095-6134.2010.3.002

带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解

窦井波

西安财经学院统计学院, 西安 710100

收稿日期:2009-09-25 修回日期:2009-12-14 发布日期:2010-05-15
通讯作者: 窦井波
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

DOU Jing-Bo

School of Statistics, Xian University of Finance and Economics, Xian 710100, China

Received:2009-09-25 Revised:2009-12-14 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) 

摘要/Abstract

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 - Δ u-μ u |x|² =λu+K(x) |u|^{2^*(s)-2}u |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

Abstract:

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)-2}u |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.

Key words: Hardy-Sobolev critical exponent, semilinear elliptic equation, linking theorem, nontrivial solution

中图分类号:

O175.25

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.

DOU Jing-Bo. Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight[J]. , 2010, 27(3): 306-313.

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带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解

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

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