| 含多重临界位势的渐近线性椭圆方程的正解 |
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| 引用本文： | 沈尧天,刘爱荣,翟永红.含多重临界位势的渐近线性椭圆方程的正解[J].华南理工大学学报(自然科学版),2006,34(11):105-108. |
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| 作者姓名： | 沈尧天 刘爱荣 翟永红 |
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| 作者单位： | 1. 华南理工大学,数学科学学院,广东,广州,510640
2. 广州安迅经济发展有限公司,广东,广州,510420 |
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| 基金项目： | 国家自然科学基金资助项目(10471047) |
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| 摘 要： | 在新Sobolev-Hardy空间中讨论含多重临界位势的渐近线性椭圆方程正解的存在性.该方程的非线性项是渐近线性的,不满足Ambrosetti-Rabinowitz条件.文中运用没有Palais-Smale条件的山路引理证明了在较弱的条件下,方程至少存在一个正解.
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| 关 键 词： | 山路引理 渐近线性 椭圆方程 正解 存在性 强收敛 |
| 文章编号： | 1000-565X（2006）11-0105-04 |
| 收稿时间： | 2005-12-13 |
| 修稿时间： | 2005年12月13 |
Positive Solution to Asymptotically Linear Elliptic Equation with Multiple Critical Potentials |
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| Shen Yao-tian,Liu Ai-rong,Zhai Yong-hong.Positive Solution to Asymptotically Linear Elliptic Equation with Multiple Critical Potentials[J].Journal of South China University of Technology(Natural Science Edition),2006,34(11):105-108. |
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| Authors: | Shen Yao-tian Liu Ai-rong Zhai Yong-hong |
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| Institution: | 1. School of Mathematical Sciences, South China Univ. of Tech. , Guangzhou 5106d0, Guangdong, China; 2. Guangzhou Anxun Economic Development Co. ,Ltd., Guangzhou 510420, Guangdong, China |
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| Abstract: | This paper discusses the existence of the positive solution to an asymptotically linear elliptic equation with multiple critical potentials in Sobolev-Hardy space.As the right term of the equation is asymptotically linear and does not satisfy the Ambrosetti-Rabinowitz condition,the Mountain Pass Theorem without Palais-Smale condition is used to prove that the equation is of at least one positive solution in a weaker condition. |
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| Keywords: | Mountain Pass Theorem asymptotical linearity elliptic equation positive solution existence strong convergence |
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