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 系統識別號 U0002-1806201215364200 中文論文名稱 廣義區間上動態方程的存在性與穩定性 英文論文名稱 Existence and Stability for Dynamic Equation on Time Scales 校院名稱 淡江大學 系所名稱(中) 數學學系博士班 系所名稱(英) Department of Mathematics 學年度 100 學期 2 出版年 101 研究生中文姓名 林尚文 研究生英文姓名 Shang-Wen Lin 學號 893150044 學位類別 博士 語文別 英文 口試日期 2012-06-01 論文頁數 52頁 口試委員 指導教授-錢傳仁委員-王富祥委員-林賜德委員-張茂盛委員-陳建隆 中文關鍵字 廣義區間  二階常微分方程  兩點邊界值問題  劣線性  超線性  Schauder固定點定理  Lyapunov穩定性  隱函數方程 英文關鍵字 Time scales  Green's function  Arzela-Ascoli theorem  Schauder fixed point theorem  sublinear  suplinear  Lyapunov Stability  Implicit Dynamic Equations  Index 1 學科別分類 中文摘要 本論文主要分兩個部分。首先，我們探討廣義區間上二階非線性常微分方程，搭配兩點邊界值條件之下正解的存在性，並進一步以劣線性及超線性的觀點提出關於外力項的限制條件。此外，將本文的結果應用於連續型的方程，也能將先前的研究結果加以推廣。 其次，我們探討類線性隱函數方程之零解的穩定性。我們先以指標的概念處理存在性，再進一步以Lyapunov函數討論其穩定性。 英文摘要 In this thesis,we give a criterion for the existence of positive solutions for nonlinear second order ordinary differential equations with two-point boundary value conditions on time scales. Moreover, for some source terms which are in the sense of sublinear or superlinear, we also formulate corollaries and examples for applications and we improve previous results. Second, we investigate the stability of the solution x=0 for a class of quasilinear implicit dynamic equations on time scales of the form \$A_tx^{Delta}=f(t,x)\$. We deal with an index concept to study the solvability and use Lyapunov functions as a tool to approach the stability problem. 論文目次 1.Introduction.............................................1 2.Some Basic Notations of the Theory of the Analysis on Time Scales................................................3 3.Nonlinear two-point boundary value problems on time scales.....................................................7 3.1Introduction............................................7 3.2Some preliminaries and main result......................8 3.3Consequence and examples...............................11 4.Lyapunov Stability of Quasilinear Implicit Dynamic Equations on Time Scales..................................16 4.1Introduction...........................................16 4.2Nonlinear Implicit Dynamic Equations on Time Scales....................................................18 4.3Quasilinear Implicit Dynamic Equations.................27 4.4Stability Theorem of Implicit Dynamic Equations........31 4.5Conclusion.............................................48 Reference.................................................49 參考文獻  R. 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Wirth, A spectral characterization of exponential stability for linear time-invariant systems on time scales, Discrete and Continuous Dynamic Systems, vol. 9, no. 5, pp. 1223-1241, 2003.  Christopher C. Tisdell, Atiya Zaidi, Basic qualitative and quantitative results for solutions to nonlinear, dynamic equations on time scales with an application to economic modeling, Nonlinear Analysis, 68 (2008) 3504-3524. 論文使用權限 同意紙本無償授權給館內讀者為學術之目的重製使用，於2012-06-25公開。同意授權瀏覽/列印電子全文服務，於2012-06-25起公開。 若您有任何疑問，請與我們聯絡！圖書館： 請來電 (02)2621-5656 轉 2487 或 來信 dss@mail.tku.edu.tw 