# 一类二阶奇异微分方程解的最大存在区间The Largest Existentially Definable Interval of a Class of Second Order Singular Differential Equations

DOI: 10.12677/AAM.2017.65079, PDF, HTML, XML, 下载: 951  浏览: 2,299

Abstract: In this thesis, we investigate the largest existentially definable interval for the solutions of a class of second order singular differential equations. In the first part, we show the meaning for studying the existence of solutions of ordinary differential equations, some important existence theorems and the largest existentially definable interval theorems for solutions. In the second part, we study the largest existentially definable interval of a class of second order singular differential equations.

 [1] 李文林. 数学史教程[M]. 北京: 高等教育出版社, 2004: 3-14. [2] 王树禾. 数学思想史[M]. 北京: 国防工业出版社, 2003: 2-23. [3] 白阿拉坦高娃. 一维奇异微分方程的混合有限元方法[D]: [硕士学位论文]. 呼和浩特: 内蒙古大学, 2011. [4] Wang, Z. and Ma, T. (2012) Existence and Multiplicity of Periodic Solutions of Semilinear Resonant Duffing Equations with Singularities. Nonlinearity, 25, 279. https://doi.org/10.1088/0951-7715/25/2/279 [5] Wang, Z. (2014) Lazer-Leach Type Conditions on Periodic Solutions of Semilinear Resonant Duffing Equations with Singularities. Zeitschrift Für Angewandte Mathematik Und Physik, 65, 69-89. https://doi.org/10.1007/s00033-013-0323-3 [6] Jiang, W., Huang, X., Guo, W., et al. (2013) The Existence of Positive Solutions for the Singular Fractional Differential Equation. Journal of Applied Mathematics & Computing, 41, 171-182. https://doi.org/10.1007/s12190-012-0603-7 [7] Vong, S.W. (2013) Positive Solutions of Singular Fractional Differential Equ-ations with Integral Boundary Conditions. Mathematical & Computer Modelling, 57, 1053-1059. https://doi.org/10.1016/j.mcm.2012.06.024 [8] Han, Z. (2012) Uniqueness of Positive Solutions for Boundary Value Problems of Singular Fractional Differential Equations. Inverse Problems in Science & Engineering, 20, 299-309. https://doi.org/10.1080/17415977.2011.603726 [9] 刘小林. 一类奇异微分方程解的正则性及其应用[D]: [博士学位论文]. 北京: 清华大学, 2013. [10] 蒋继强. 非线性奇异微分方程边值问题的正解及其应用[D]: [博士学位论文]. 曲阜: 曲阜师范大学, 2013. [11] 丁同仁, 李承治. 常微分方程教程[M]. 北京: 高等教育出版社, 1991: 7-23. [12] 丁同仁. 常微分方程定性方法的应用[M]. 北京: 高等教育出版社, 2004: 8-31. [13] 弭鲁芳, 纪在秀. 论一类常微分方程解的最大存在区间[J]. 聊城大学学报, 2006, 19(4): 24-26. [14] 孔志宏, 米芳. 微分方程解的存在区间的确定[J]. 大学数学, 2013, 29(5): 71-80.