| Existence and non-existence of solutions for a class of Monge-Ampere equations |
| Zhang, Zhitao ; Wang, Kelei
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| 2009-04-01
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| 发表期刊 | JOURNAL OF DIFFERENTIAL EQUATIONS
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| ISSN | 0022-0396
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| 卷号 | 246期号:7页码:2849-2875 |
| 摘要 | We study the boundary Value problems for Monge-Ampere equations: det D(2)u = e(-u) in Omega subset of R(n), n >= 1, u vertical bar(partial derivative Omega) = 0. First we prove that any solution on the ball is radially symmetric by the argument of moving plane. Then we show there exists a critical radius such that if the radius of a ball is smaller than this critical value there exists a Solution, and vice versa. Using the comparison between domains we can prove that this phenomenon occurs for every domain. Finally we consider an equivalent problem with a parameter det D(2)u = e(-tu) in Omega, u vertical bar(partial derivative Omega) = 0, t >= 0 . By using Lyapunov-Schmidt reduction method we get the local structure of the solutions near a degenerate point: by Leray-Schauder degree theory, a priori estimate and bifurcation theory we get the global structure. (C) 2009 Elsevier Inc. All rights reserved. |
| 关键词 | Monge-Ampere equations
Moving plane
Implicit Function Theorem
Leray-Schauder degree theory
Bifurcation
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| DOI | 10.1016/j.jde.2009.01.004
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| 语种 | 英语
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| WOS研究方向 | Mathematics
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| WOS类目 | Mathematics
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| WOS记录号 | WOS:000264572500013
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| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE
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| 引用统计 |
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| 文献类型 | 期刊论文
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| 条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/9163
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| 专题 | 数学所
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| 通讯作者 | Zhang, Zhitao |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
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推荐引用方式
GB/T 7714 |
Zhang, Zhitao,Wang, Kelei. Existence and non-existence of solutions for a class of Monge-Ampere equations[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2009,246(7):2849-2875.
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| APA |
Zhang, Zhitao,&Wang, Kelei.(2009).Existence and non-existence of solutions for a class of Monge-Ampere equations.JOURNAL OF DIFFERENTIAL EQUATIONS,246(7),2849-2875.
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| MLA |
Zhang, Zhitao,et al."Existence and non-existence of solutions for a class of Monge-Ampere equations".JOURNAL OF DIFFERENTIAL EQUATIONS 246.7(2009):2849-2875.
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