高阶线性微分方程解的完全正规增长性

数学物理学报 ›› 2023, Vol. 43 ›› Issue (3): 733-742.

高阶线性微分方程解的完全正规增长性

陈丽,刘慧芳^*()

江西师范大学数学与统计学院南昌 330022

收稿日期:2022-08-08 修回日期:2022-11-18 出版日期:2023-06-26 发布日期:2023-06-01
通讯作者: 刘慧芳 E-mail:liuhuifang73@sina.com
基金资助:
国家自然科学基金(12261044);国家自然科学基金(11661044);江西省教育厅科技项目(GJJ210302)

The Completely Regular Growth of Solutions of Higher Order Linear Differential Equations

Chen Li,Liu Huifang^*()

School of Mathematics and Statistics, Jiangxi Normal University, Nanchang 330022

Received:2022-08-08 Revised:2022-11-18 Online:2023-06-26 Published:2023-06-01
Contact: Huifang Liu E-mail:liuhuifang73@sina.com
Supported by:
NSFC(12261044);NSFC(11661044);STP of Education Department of Jiangxi Province(GJJ210302)

摘要/Abstract

摘要：

研究高阶线性微分方程完全正规增长性解的存在性, 其中方程的控制系数为指数多项式. 运用指数多项式的Nevanlinna特征, 得到方程不存在完全正规增长性解的判定条件. 同时, 对具有指数多项式解的高阶线性微分方程, 给出了方程解的表示形式与控制系数之间的关系.

关键词: 线性微分方程, 完全正规增长性, 指数多项式, 整函数

Abstract:

In this paper, the existence of completely regular growth solutions of higher order linear differential equations is studied, where its dominant coefficient is an exponential polynomial. By using the Nevanlinna characteristic of exponential polynomials, some conditions which guarantee the non-existence of such solutions are obtained. At the same time, for the higher order linear differential equation with exponential polynomial solutions, the relationship between the expression of its solutions and dominant coefficient is given.

Key words: Linear differential equation, Completely regular growth, Exponential polynomial, Entire function

中图分类号:

O174.52

陈丽,刘慧芳. 高阶线性微分方程解的完全正规增长性[J]. 数学物理学报, 2023, 43(3): 733-742.

Chen Li,Liu Huifang. The Completely Regular Growth of Solutions of Higher Order Linear Differential Equations[J]. Acta mathematica scientia,Series A, 2023, 43(3): 733-742.

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