| 带Hardy-Sobolev临界指数和权函数的半线性椭圆问题的非平凡解 |
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| 引用本文： | 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].中国科学院研究生院学报,2010,27(3):306-313. |
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| 作者姓名： | 窦井波 |
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| 作者单位： | 西安财经学院统计学院,西安,710100 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (10802061); Natural Science Basic Research Plan in Shaanxi Province of China(SJ08F27) |
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| 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)-2u |x|s , x∈Ω; u=0, x∈Ω, 解的存在性,其中Ω是 R 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.
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| 关 键 词： | Hardy-Sobolev临界指数 半线性椭圆方程 环绕定理 非平凡解 |
| 收稿时间： | 2009-09-25 |
| 修稿时间： | 2009-12-14 |
Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight |
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| DOU Jing-Bo.Nontrivial solutions for semilinear elliptic problems with Hardy-Sobolev critical exponents and a weight[J].Journal of the Graduate School of the Chinese Academy of Sciences,2010,27(3):306-313. |
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| Authors: | DOU Jing-Bo |
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| Institution: | School of Statistics, Xian University of Finance and Economics, Xian 710100, China |
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| Abstract: | 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{-△u-μ(u/|x|=λu+K(x)(|u|2*(s)-2u/|x|s,x∈Ω;u=0,x∈(ζ)Ω)),where Ω is an open bounded domain of RN with smooth boundary (ζ)Ω and 0∈Ω,N≥5,0≤s≤2,0≤μ≤((n-2)/2)2,λ＞0,and K(χ)is a bounded positive function on Ω. |
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| Keywords: | Hardy-Sobolev critical exponent semilinear elliptic equation linking theorem nontrivial solution |
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