| 引用本文: | 周海银.零扰动下一类RN 上临界增长的椭圆方程正解的存在性.[J].国防科技大学学报,1992,14(3):89-95.[点击复制] |
| Zhou Haiyin.The Exisitence of Positive Solutions of a Quasilinear Elliptic Equation on RN of Critical Increase with Zero-perturbation[J].Journal of National University of Defense Technology,1992,14(3):89-95[点击复制] |
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| 零扰动下一类RN 上临界增长的椭圆方程正解的存在性 |
| 周海银 |
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(系统工程与应用数学系)
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| 摘要: |
| 本文讨论了N 维欧氏空间RN上一类临界增长的拟线性椭圆型方程-div (︱Du︱p-2Du)+k(x)up-1=K(x)up-1，u∈W1,p(RN)∩Lp(RN)的正解的存在性。其中4≤p2≤N,p=Np/(N-p)。在微分几何与物理学等领域起重要作用的 Yamabe 问题就是其特例 (p=2)。本文运用集中紧引理，证明了问题的正解的存在性。 |
| 关键词: 椭圆方程，方程解，存在性，临界增长 |
| DOI： |
| 投稿日期：1991-06-06 |
| 基金项目: |
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| The Exisitence of Positive Solutions of a Quasilinear Elliptic Equation on RN of Critical Increase with Zero-perturbation |
| Zhou Haiyin |
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(Department of System Engineering and Applied Mathematics)
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| Abstract: |
| This Paper is concerned with the existence of positive solutions. The Yamabe problem which is very important in the fields of differential geometry，physics，etc is a special example. In this paper，the author has obtained the existence of positive solutions of the above problem by applying the concentrain-compactness lemmas. |
| Keywords: elliptic equation,soltion of equation,existence |
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