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| 研究生： |
梁益昌 Liang, Yi Chang |
|---|---|
| 論文名稱： |
一階衝擊動態方程的週期邊界值問題 PBVPs of first-order impulsive dynamic equations on time scales |
| 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： | 2009 |
| 畢業學年度： | 97 |
| 語文別： | 英文 |
| 論文頁數： | 24 |
| 中文關鍵詞： | 時間序列 、週期邊界值問題 、衝擊動態方程 、Green函數 、Schaefer定理 、Banach固定點定理 |
| 外文關鍵詞： | Time scale, Periodic boundary value problem, Impulsive dynamic equation, Green's function, Schaefer's theorem, Banach's fixed point theorem |
| 相關次數： | 點閱：124 下載：57 |
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在這篇論文中，我們討論的是一階非線性衝擊動態方程的週期邊界值問題。利用Schaefer定理及Banach固定點定理，我們得到一些解的存在性結果。
In this thesis, we are concernd with nonlinear first-order periodic boundary
value problems of impulsive dynamic equations on time scales. By
using Schaefer’s theorem and Banach’s fixed point theorem we acquire
some new existence results.
Contents
謝 辭 i
Abstract ii
中文摘要 iii
1 Introduction 1
2 Preliminary 3
3 Linear Problem 5
4 Nonlinear Problem 7
5 Examples 20
References 23
[1] D.D. Bainov, P.S. Simeonov, Systems with Impulse Effect: Stability Theory and
Applications. Horwood, Chichester, (1989)
[2] D.D. Bainov, P.S. Simeonov, Impulsive Differential Equations: Periodic
Solutions and Applications. Longman Scientific and Technical, Harlow, (1993)
[3] V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive
Differential Equations. World Scientific, Singapore, (1989)
[4] J.J. Nieto, Basic theory for nonresonance impulsive periodic problems of first
order, J. Math. Anal. Appl. 205 (1997) 423-433.
[5] J.J. Nieto, Impulsive resonance periodic problems of first order, Appl. Math.
Lett. 15 (2002) 489-493.
[6] J.J. Nieto, Periodic boundary value problems for first order impulsive ordinary
differential equations, Nonlinear Appl. 51 (2002) 1223-1232.
[7] D. Franco, J.J. Nieto, Maximum principles for periodic impulsive first order
problems, J. Comput. Appl. Math. 88 (1998) 144-159.