DC Field | Value | Language |
dc.contributor | 王振男 | zh-TW |
dc.contributor | 臺灣大學:數學研究所 | zh-TW |
dc.contributor.author | 謝昇諺 | zh-TW |
dc.contributor.author | Hsieh, Sheng-Yen | en |
dc.creator | 謝昇諺 | zh-TW |
dc.creator | Hsieh, Sheng-Yen | en |
dc.date | 2009 | en |
dc.date.accessioned | 2010-05-05T10:50:59Z | - |
dc.date.accessioned | 2018-06-28T09:14:25Z | - |
dc.date.available | 2010-05-05T10:50:59Z | - |
dc.date.available | 2018-06-28T09:14:25Z | - |
dc.date.issued | 2009 | - |
dc.identifier.other | U0001-2506200907083300 | en |
dc.identifier.uri | http://ntur.lib.ntu.edu.tw//handle/246246/180658 | - |
dc.description.abstract | 這篇文章介紹了節點域定理。對於調和函數的特徵值問題,第N個特徵函數的節點域個數K(u_N),小於或等於N. 對於二階橢圓特徵值問題,當維度d大於等於3且主要係數A是Holder連續時,K(u_N) 小於等於 2(N-1)。對於二階橢圓Stekloff特徵值問題,當d = 2且A是L^1或是d大於等於3且A是Lipschitz時,K(u_N)小於等於N。對於雙調和函數的特徵值問題,當d = 1,K(u_N)小於等於N. 然而,對於d大於等於2,這一般不會成立。最後,我們用Krein-Rutman定理來討論主要特徵函數的同號性。 | zh-TW |
dc.description.abstract | This article introduces the nodal domain theorem. For harmonic eigenvalue problem, the number of nodal domain of N-th eigenfunction, K(u_N), less than N. For second orderlliptic eigenvalue problem, when dimension d is greater than or equal to 3 and the principal coeffcient A is Holderontinuous, K(u_N) is less than or equal to 2(N-1). For second order elliptic Stekloff eigenvalue problem, when = 2 and A is L^1 or d is greater than or equal to 3 and A 2 is Lipschitz, K(u_N) is less than or equal to N. For biharmonic eigenvalue problem, when d = 1, K(u_N) is less than or equal to N. However, it generally not holds for d is greater than or equal to 2. Finally, we use Krein-Rutman theorem to discuss the one-sign property of principal eigenfunction. | en |
dc.description.tableofcontents | 口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Introduction: 1 Second order elliptic eigenvalue problems: 2 Second order elliptic Steklo eigenvalue problem 8 Biharmonic eigenvalue problem 12 Principal eigenvalue 13考文獻19 | en |
dc.format | application/pdf | en |
dc.format.extent | 574330 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.language | en | en |
dc.language.iso | en_US | - |
dc.subject | 斯特克羅夫 | zh-TW |
dc.subject | 特徵值問題 | zh-TW |
dc.subject | 節點域定理 | zh-TW |
dc.subject | Stekloff | en |
dc.subject | Steklov | en |
dc.subject | eigenvalue problem | en |
dc.subject | nodal domain | en |
dc.title | 節點域定理和相關的主題 | zh-TW |
dc.title | Nodal Domain Theorem and Related Topics | en |
dc.type | thesis | en |
dc.identifier.uri.fulltext | http://ntur.lib.ntu.edu.tw/bitstream/246246/180658/1/ntu-98-R96221013-1.pdf | - |
item.languageiso639-1 | en_US | - |
item.cerifentitytype | Publications | - |
item.fulltext | with fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
item.openairetype | thesis | - |
item.grantfulltext | open | - |
Appears in Collections: | 數學系
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