Please use this identifier to cite or link to this item:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43413
Title: | 節點域定理和相關的主題 Nodal Domain Theorem and Related Topics |
Authors: | Sheng-Yen Hsieh 謝昇諺 |
Advisor: | 王振男 |
Keyword: | 斯特克羅夫,特徵值問題,節點域定理, Stekloff,Steklov,eigenvalue problem,nodal domain, |
Publication Year : | 2009 |
Degree: | 碩士 |
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。 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 order elliptic eigenvalue problem, when dimension d is greater than or equal to 3 and the principal coeffcient A is Holder continuous, K(u_N) is less than or equal to 2(N-1). For second order elliptic Stekloff eigenvalue problem, when d = 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. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43413 |
Fulltext Rights: | 有償授權 |
Appears in Collections: | 數學系 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
ntu-98-1.pdf Restricted Access | 560.87 kB | Adobe PDF |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.