高阶线性微分方程解与其小函数的增长性

上海交通大学学报（自然版） ›› 2013, Vol. 47 ›› Issue (07): 1155-1159.

高阶线性微分方程解与其小函数的增长性

金瑾

（毕节学院数学系，贵州毕节 551700）

收稿日期:2012-09-24 出版日期:2013-07-30 发布日期:2013-07-30
基金资助:
贵州省科学技术基金资助项目(2012GZ10526,2012GZ10526),贵州省毕节地区科研基金资助项目(［2011］02)

Growth of Solutions of Higher Order Linear Differential Equations and Its Small Functions

JIN Jin

(Mathematics Department, Bijie University, Bijie 551700, Guizhou, China)

Received:2012-09-24 Online:2013-07-30 Published:2013-07-30

摘要/Abstract

摘要：

利用整函数的Nevanlinna值分布理论和复微分方程的研究技巧，研究了高阶齐次线性微分方程解的增长性,探讨了高阶齐次线性微分方程解以及它们的一阶、二阶导数与小函数之间关系，得到了微分方程解以及它们的一阶、二阶导数与小函数零点的精确估计，推广和改进了一些文献中的结论.

关键词: 线性微分方程, 整函数, 小函数, 收敛指数

Abstract:

The growth of solutions to higher order linear differential equations and its small functions was investigated using the Nevanlinna value distribution theory of entire functions and the investigation skills of complex differential equations. The relation between the 1st, 2nd derivatives and the small functions was discussed, and precise estimate was obtained, which improved and generalized some results in literature.

Key words: linear differential equations； entire function； small function, exponent of convergence

中图分类号:

O 174.5

金瑾. 高阶线性微分方程解与其小函数的增长性[J]. 上海交通大学学报（自然版）, 2013, 47(07): 1155-1159.

JIN Jin. Growth of Solutions of Higher Order Linear Differential Equations and Its Small Functions[J]. Journal of Shanghai Jiaotong University, 2013, 47(07): 1155-1159.

参考文献

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