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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/95632


    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/95632


    Title: 一些非自控Emden-Fowler微分方程之研究
    Studies on some nonautonomous emden-fowler differential equations
    Authors: 李宣緯
    Contributors: 符聖珍
    李宣緯
    Keywords: 方程轉換
    震盪解
    爆破解
    Date: 2010
    Issue Date: 2016-05-09 16:41:52 (UTC+8)
    Abstract: 因有數學符號，無法顯示於此。
    Abstract......1
    中文摘要.....2

    1. Introduction.....3

    2. Transformation for a Nonautonomous Ordinary Di erential Equation.....5
    2.1 Goals and Previous Results.....5
    2.2 Main Results.....7

    3. The Solutions for Initial Value Problems and Boundary Value Problems.....12
    3.1 Existence and Uniqueness of Initial Value Problem.....12
    3.2 Initial Value Problem.....14
    3.3 Two-Point Boundary Value Problem.....19
    3.4 Three-Point Boundary Value Problem.....19

    4. Blow-up Solutions.....21
    4.1 On the Scalar Differential Equations.....21
    4.2 Estimates for the Life Span of Blow-up Solution.....25
    4.3 Properties of Parameters that Affect the Blow-up Time.....28

    5. Simulation and Comparison.....32
    5.1 Numerical and Approximation Method for the Oscillatory Case.....32
    5.2 Numerical and Approximation Method for the Blow-up Case.....37
    5.3 Numerical Estimation of Blow-up Time....38

    6. Conclusion.....41
    Reference: [1] Richard Bellman. Stability Theory of Differential Equations. McGraw-Hill Book Company, 1953.
    [2] L. M. Berkovich. The Generalized Emden-Fowler Equation. Symmetry in Nonlinear Mathematical Physics, 1:155{163, 1997.
    [3] Y. C. Chen and L. Y. Tsai. Blow-up Solutions of Nonlinear Differential Equations.
    Applied Mathematics and Computation, 169:366{387, 2005.
    [4] A. Gricans and F. Sadyrbaev. Lemniscatic Functions in the Theory of the Emden-Fowler Differential Equation. Proceedings Institute of Mathematical and Computer Science, 3, 2003.
    [5] A. Gricans and F. Sadyrbaev. Explict Solutions of Non-Autonomous Emden-Fowler Type Equations. Proceedings Institute of Mathematical and Computer Science, 5:5{23, 2005.
    [6] S. Ogorodnikova and F. Sadyrbaev. Estimation of the Number of Solutions to the Nonlinear Second Order Boundary Value Problems. Proceedings Institute of Mathematical and Computer Science, 5:24{32, 2005.
    [7] S. Ogorodnikova and F. Sadyrbaev. Planar Systems with Critical Points: Multiple Solutions of Two-point Nonlinear Boundary Value Problems. Nonlinear Analysis, 63:243{246, 2005.
    [8] Edmund Pinney. The Nolinear Differential Equation y`` + p(x)y + cy^3 = 0. Proceedings of the American Mathematical Society, page 681, 1950.
    [9] James L. Reid. Homogeneous Solution of a Nonliear Differential Equation. Proceedings of the American Mathematical Society, 38:532{536, 1973.
    [10] Shepley L. Ross. Differential Equations. Wiley, 1984.
    [11] P. L. Sachdev. Nonlinear Ordinary Differential Equations and Their Applications. M. Dekker, 1991.
    Description: 碩士
    國立政治大學
    應用數學系
    97751007
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0097751007
    Data Type: thesis
    Appears in Collections:[應用數學系] 學位論文

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