| 全空间上一类带Hardy项的半线性椭圆方程 |
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| 引用本文： | 魏娜,蒋永生,何琪.全空间上一类带Hardy项的半线性椭圆方程[J].应用数学,2012,25(3):616-623. |
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| 作者姓名： | 魏娜 蒋永生 何琪 |
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| 作者单位： | 1. 中南财经政法大学统计与数学学院,湖北武汉,430073
2. 浙江大学竺可桢学院,浙江杭州,310058 |
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| 基金项目： | 数学天元青年基金(11126313);中南财经政法大学引进人才科研启动基金(31540911209) |
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| 摘 要： | 本文讨论如下一类半线性椭圆方程非平凡解的存在性.-Δu-μu/(|x|2)+u=|u|2*-2u+k(x)f(u),x∈RN,u∈H1(R~N),其中N≥3,0<μ<(N-2)/2]2,2*=2N/(N-2),k(x)∈C(RN,R),函数f(u)关于自变量u在无穷远处渐近线性或者超线性.
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| 关 键 词： | 紧性 临界Sobolev指标 椭圆方程 |
On a Semilinear Elliptic Equation with Hardy Potential and Critical Nonlinearities in R~N |
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| WEI Na
,
JIANG Yongsheng
,
HE Qi.On a Semilinear Elliptic Equation with Hardy Potential and Critical Nonlinearities in R~N[J].Mathematica Applicata,2012,25(3):616-623. |
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| Authors: | WEI Na JIANG Yongsheng HE Qi |
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| Institution: | 1.School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,China;2.School of Zhu Kezhen,Zhejiang University,Hangzhou 310058,China) |
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| Abstract: | In this paper,we are concerned with the existence of the solution of the following nonlinear equation-Δu-μu/(|x|2)+u=|u|2*-2u+k(x)f(u),x∈RN,u∈H1(RN),where N≥3,0<μ<(N-2)/2]2,2*=2N/(N-2),k(x)∈C(RN,R),and f(u) is either asymptotically linear or superlinear in u as |u|→∞. |
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| Keywords: | Compactness Critical Sobolev exponent Elliptic equation |
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