单位圆内二阶线性微分方程解的导数的不动点
The Fixed Points of the Solutions and Their Derivatives of Second Order Linear Differential Equation in the Unit Disc
DOI: 10.12677/PM.2017.76062, PDF,    国家自然科学基金支持
作者: 陈 玉*：江西师范大学数学与信息科学学院，江西 南昌
关键词: 线性微分方程；单位圆；解析函数；不动点；超级；Linear Differential Equation； Unit Disc； Analytic Functions； Fixed Points； Hyper Order
摘要: 本文研究了一类二阶线性微分方程 的解及其导数的不动点性质，其中A(z)和B(z)是单位圆 内的解析函数，得到了解及其一阶、二阶导数的不动点的精确估计。
Abstract: The properties of the fixed points of the solutions and their derivatives of a type of second order linear differential equation , where A(z) and B(z) are analytic functions in the unit disc , are investigated. We obtain some precise estimates of the fixed points of the solutions and their 1st, 2nd derivatives of the equations.
文章引用：陈玉. 单位圆内二阶线性微分方程解的导数的不动点[J]. 理论数学, 2017, 7(6): 471-477. https://doi.org/10.12677/PM.2017.76062

参考文献

[1] Hayman, W. (1964) Meromorphic Functions. Clarendon Press, Oxford.
[2] Yang, L. (1993) Value Distribution Theory. Sprin-ger-Verlag, Berlin. Science Press, Beijing.
[3] Heittokangas J. (2000) On Complex Differential Equations in the Unit Disc. Annales Academiæ Scientiarum Fennicæ Mathematica Dissertationes, 122, 1-54.
[4] Tsuji M. (1975) Potential Theory in Modern Function Theory. Chelsea, New York, Reprint of the 1959 Edition.
[5] 李叶舟. 单位圆盘上二阶微分方程解的增长性[J]. 纯粹数学与应用数学, 2002, 18(4): 295-300.
[6] 曹廷彬, 仪洪勋. 关于单位圆内解析系数的二阶线性微分方程的复振荡[J]. 数学年刊: A辑, 2007, 28(5): 719- 732.
[7] 曹廷彬, 仪洪勋. 关于单位圆内解析系数的线性微分方程的复振荡理论[J]. 数学物理学报: A辑, 2008, 28(6): 1046-1057.
[8] 甘会林, 孔荫莹. 单位圆内二阶线性微分方程的解及其导数的不动点[J]. 江西师范大学学报(自然科学版), 2008, 32(6): 671-673.
[9] Cao, T.B. (2009) The Growth, Oscillation and Fixed Points of Solutions of Complex Linear Differential Equations in the Unit Disc. Journal of Mathematical Analysis and Applications, 352, 739-748.
https://doi.org /10.1016/j.jmaa.2008.11.033
[10] Belaïdi, B. (2010) Oscillation of Fast Growing Solutions of Linear Differential Equations in the Unit Disc. Acta Universitatis Sapientiae, Mathematica, 2, 25-38.
[11] Fenton, P., Gröhn, J., Heittokangas, J., Rossi, J., and Rättyä, J. (2014) On α-Polynomial Regular Functions, with Applications to Ordinary Differential Equations. Proceedings of the Edinburgh Mathematical Society, 57, 405-421.
https://doi.org /10.1017/S0013091514000017

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