| 具Hardy-Sobolev临界指数椭圆方程的非平凡解 |
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| 引用本文： | 沈自飞,杨敏波.具Hardy-Sobolev临界指数椭圆方程的非平凡解[J].数学学报,2005,48(5):999-101. |
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| 作者姓名： | 沈自飞 杨敏波 |
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| 作者单位： | [1]浙江师范大学数学系,金华321004 [2]北京信息控制研究所,北京100037 |
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| 基金项目： | 国家自然科学基金资助项目（10471113）;浙江省自然科学基金资助项目（M103098） |
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| 摘 要： | 运用精确估计和变分法得到具奇异位势的椭圆方程-△u-μu/|x|2=|u|2*(s)-2u/|x|s+λu,u∈H0(1,2)(Ω)的非平凡解的存在性,其中Ω是有光滑边界的有界开区域,μ,λ是两个正参数.
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| 关 键 词： | 非平凡解 Hardy-Sobolev临界指数 Palais-Smale序列 |
| 文章编号： | 0583-1431（2005）05-0999-12 |
| 收稿时间： | 2004-10-28 |
| 修稿时间： | 2004-10-282005-03-15 |
Nontrivial Solutions for Hardy-Sobolev Critical Elliptic Equations |
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| Shen ZiFei;Yang MinBo.Nontrivial Solutions for Hardy-Sobolev Critical Elliptic Equations[J].Acta Mathematica Sinica,2005,48(5):999-101. |
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| Authors: | Shen ZiFei;Yang MinBo |
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| Institution: | Zi Pei SHEN Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China Beijing Institute of Information and Control, Beijing 100037, P. R. China Min Bo YANG Department of Mathematics, Zhejiang Normal University, Jinhua 321004, P. R. China |
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| Abstract: | With the aids of variational methods and delicate estimates, the existence of nontrivial solutions is obtained for elliptic equations with singular potential-△u-μ u/|x|2=|u|2*(s)-2u/|x|s+ λu,u∈H0 (1,2)(Ω)where Ωis an open bounded domain with smooth boundary,μ,λA are two positive parameters. |
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| Keywords: | Nontrivial solution Hardy Sobolev critical Palais Smale sequence |
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