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| 研究生： |
黃雅雯 Huang, Ya Wen |
|---|---|
| 論文名稱： |
二維非線性動態系統之非振盪解的分類法 A Classification Scheme for Nonoscillatory Solutions of Two-Dimensional Nonlinear Dynamical Systems |
| 指導教授： | 符聖珍 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2012 |
| 畢業學年度： | 101 |
| 語文別： | 中文 |
| 論文頁數： | 25 |
| 中文關鍵詞： | 非振盪性解的分類 |
| 外文關鍵詞： | Nonoscillatory Solutions, Nonlinear Dynamical System |
| 相關次數： | 點閱：64 下載：15 |
| 分享至: |
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在此篇論文中，我們提供二維非線性動態系統之非振盪解的一個分類法，此分類法是依據解的漸近值作分類，同時我們也得到具有此漸近值之非振盪解的存在性的充分必要條件。
In this thesis, we provide a classification scheme for nonoscillatory solutions of a class of two-dimensional dynamical systems in terms of their asymptotic values.
In addition, we find the sufficient and necessary conditions for the existence of these solutions.
Contents
謝辭 .......................................... i
Abstract .................................... iii
中文摘要 .................................. iv
Content ................................... v
1. Introduction .............................................. 1
2. The Fundamental Theory of Time Scales ....... 2
3. Preparatory Lemmas ................................... 5
4. The Main Results ......................................... 9
5. Reference ................................................... 19
M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhauser, Boston (2001)
Douglas R. Anderson, Oscillation and nonoscillation criteria for two-dimensional time-scale systems of first-Order nonlinear dynamic equations, Electronic Journal of Differential Equations, 24 (2009), 1-13
Douglas R. Anderson and William R. Hall, Oscillation criteria for two-dimensional systems of first-order linear dynamic equations on time scales, Involve a Journal of Mathematics 2 (2009), No.1, 1-16.
B. Knaster, Un Théoréme sur les fonctions d'nensembles, Annales de la Société Polonaise de Mathématique 6 (1928), 133-134.
Walter G. Kelley and Allan C. Peterson, Difference Equations, An Introduction with Applications, Academic Press, Inc. (1991).
Youjun Xu, and Zhiting Xu, Oscillation criteria for two-dimensional dynamic systems on time scales, Journal of Computational and Applied Mathematics, 225 (2009), 9-19.
