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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43413完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王振男 | |
| dc.contributor.author | Sheng-Yen Hsieh | en |
| dc.contributor.author | 謝昇諺 | zh_TW |
| dc.date.accessioned | 2021-06-15T01:55:15Z | - |
| dc.date.available | 2009-07-14 | |
| dc.date.copyright | 2009-07-14 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-06-30 | |
| dc.identifier.citation | [1] Filippo Gazzola Alberto Ferrero and Tobias Weth. On a fourth order steklo eigenvalue
problem. [2] Giovanni Alessandrini. On courant's nodal domain theorem. Forum Math., 10:521{ 531, 1998. [3] T. Boggio. Sulle funzioni di green d'ordine m. Rend. Circ. Mat. Palermo, 20:97{135, 1905. [4] Charles V. Coffman. On the structure of solutions to 2u = u which satisfy the clamped plate conditions on a right angle. SIAM J. Math. Anal., 13(5):746{757, September 1982. [5] N.S. Trudinger D. Gilbarg. Elliptic partial di erential equations of second order. Grundlehren der mathematischen Wissenschaften. Springer-Verlag, Berlin, second edition, 1983. [6] R. Finn and D. Gilbarg. Asymptotic behavior and uniqueness of plane subsonic ows. Comm. Pure Appl. Math., 10:23{63, 1957. [7] Hans-Christoph Grunau and Fr ed eric Robert. Positivity issues of biharmonic green's functions under dirichlet boundary conditions. [8] M. G. Krein and M. A. Rutman. Linear operators leaving invariant a cone in a banach space. Transl. Amer. Math. Soc., 10:199{325, 1962. [9] A. Krzywicki N. Aronszajn and J. Szarski. A unique continuation theorem for exterior di erential forms on riemannian manifolds. Ark. Mat., 4:417{453, 1962. [10] A. Krzywicki N. Aronszajn and J. Szarski. A unique ontinuation theorem for exterior di erential forms on riemannian manifolds. Ark. Mat., 4:417{453, September 1962. [11] M. W. Steklo . Sur les probl emes fondamentaux de la physique math ematique. Ann. Sci. Ecole Norm. Sup., 19:455{490, 1902. [12] M. E. Taylor. Partial di erential equations II: qualitative studies of linear equations. Springer-Verlag, New York, 1996. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/43413 | - |
| 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 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. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T01:55:15Z (GMT). No. of bitstreams: 1 ntu-98-R96221013-1.pdf: 574330 bytes, checksum: 45ccb509c6f936a23ef89a7d1be99d89 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | 口試委員會審定書. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii 中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv 1 Introduction: 1 2 Second order elliptic eigenvalue problems: 2 3 Second order elliptic Steklo eigenvalue problem 8 4 Biharmonic eigenvalue problem 12 5 Principal eigenvalue 13 參考文獻19 | |
| dc.language.iso | en | |
| dc.subject | 節點域定理 | zh_TW |
| dc.subject | 斯特克羅夫 | zh_TW |
| dc.subject | 特徵值問題 | zh_TW |
| dc.subject | Stekloff | en |
| dc.subject | nodal domain | en |
| dc.subject | eigenvalue problem | en |
| dc.subject | Steklov | 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 | |
| dc.date.schoolyear | 97-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊全,林景隆 | |
| dc.subject.keyword | 斯特克羅夫,特徵值問題,節點域定理, | zh_TW |
| dc.subject.keyword | Stekloff,Steklov,eigenvalue problem,nodal domain, | en |
| dc.relation.page | 20 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2009-06-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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