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Please use this identifier to cite or link to this item: https://ah.lib.nccu.edu.tw/handle/140.119/95632
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dc.contributor.advisor符聖珍zh_TW
dc.contributor.author李宣緯zh_TW
dc.creator李宣緯zh_TW
dc.date2010en_US
dc.date.accessioned2016-05-09T08:41:52Z-
dc.date.available2016-05-09T08:41:52Z-
dc.date.issued2016-05-09T08:41:52Z-
dc.identifierG0097751007en_US
dc.identifier.urihttp://nccur.lib.nccu.edu.tw/handle/140.119/95632-
dc.description碩士zh_TW
dc.description國立政治大學zh_TW
dc.description應用數學系zh_TW
dc.description97751007zh_TW
dc.description.abstract因有數學符號，無法顯示於此。zh_TW
dc.description.abstractAbstract......1\r\n中文摘要.....2\r\n\r\n1. Introduction.....3\r\n\r\n2. Transformation for a Nonautonomous Ordinary Di erential Equation.....5\r\n2.1 Goals and Previous Results.....5\r\n2.2 Main Results.....7\r\n\r\n3. The Solutions for Initial Value Problems and Boundary Value Problems.....12\r\n3.1 Existence and Uniqueness of Initial Value Problem.....12\r\n3.2 Initial Value Problem.....14\r\n3.3 Two-Point Boundary Value Problem.....19\r\n3.4 Three-Point Boundary Value Problem.....19\r\n\r\n4. Blow-up Solutions.....21\r\n4.1 On the Scalar Differential Equations.....21\r\n4.2 Estimates for the Life Span of Blow-up Solution.....25\r\n4.3 Properties of Parameters that Affect the Blow-up Time.....28\r\n\r\n5. Simulation and Comparison.....32\r\n5.1 Numerical and Approximation Method for the Oscillatory Case.....32\r\n5.2 Numerical and Approximation Method for the Blow-up Case.....37\r\n5.3 Numerical Estimation of Blow-up Time....38\r\n\r\n6. Conclusion.....41-
dc.description.tableofcontentsAbstract......1\r\n中文摘要.....2\r\n\r\n1. Introduction.....3\r\n\r\n2. Transformation for a Nonautonomous Ordinary Di erential Equation.....5\r\n2.1 Goals and Previous Results.....5\r\n2.2 Main Results.....7\r\n\r\n3. The Solutions for Initial Value Problems and Boundary Value Problems.....12\r\n3.1 Existence and Uniqueness of Initial Value Problem.....12\r\n3.2 Initial Value Problem.....14\r\n3.3 Two-Point Boundary Value Problem.....19\r\n3.4 Three-Point Boundary Value Problem.....19\r\n\r\n4. Blow-up Solutions.....21\r\n4.1 On the Scalar Differential Equations.....21\r\n4.2 Estimates for the Life Span of Blow-up Solution.....25\r\n4.3 Properties of Parameters that Affect the Blow-up Time.....28\r\n\r\n5. Simulation and Comparison.....32\r\n5.1 Numerical and Approximation Method for the Oscillatory Case.....32\r\n5.2 Numerical and Approximation Method for the Blow-up Case.....37\r\n5.3 Numerical Estimation of Blow-up Time....38\r\n\r\n6. Conclusion.....41en_US
dc.source.urihttp://thesis.lib.nccu.edu.tw/record/#G0097751007en_US
dc.subject方程轉換zh_TW
dc.subject震盪解zh_TW
dc.subject爆破解zh_TW
dc.title一些非自控Emden-Fowler微分方程之研究zh_TW
dc.titleStudies on some nonautonomous emden-fowler differential equationsen_US
dc.typethesisen_US
dc.relation.reference[1] Richard Bellman. Stability Theory of Differential Equations. McGraw-Hill Book Company, 1953.\r\n[2] L. M. Berkovich. The Generalized Emden-Fowler Equation. Symmetry in Nonlinear Mathematical Physics, 1:155{163, 1997.\r\n[3] Y. C. Chen and L. Y. Tsai. Blow-up Solutions of Nonlinear Differential Equations.\r\nApplied Mathematics and Computation, 169:366{387, 2005.\r\n[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.\r\n[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.\r\n[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.\r\n[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.\r\n[8] Edmund Pinney. The Nolinear Differential Equation y`` + p(x)y + cy^3 = 0. Proceedings of the American Mathematical Society, page 681, 1950.\r\n[9] James L. Reid. Homogeneous Solution of a Nonliear Differential Equation. Proceedings of the American Mathematical Society, 38:532{536, 1973.\r\n[10] Shepley L. Ross. Differential Equations. Wiley, 1984.\r\n[11] P. L. Sachdev. Nonlinear Ordinary Differential Equations and Their Applications. M. Dekker, 1991.zh_TW
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