一些非自控Emden-Fowler微分方程之研究

Abstract

因有數學符號，無法顯示於此。

Abstract......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