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 |
(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 |
(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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