一类高阶线性微分方程解的增长性

doi:10.13371/j.cnki.chin.q.j.m.2016.04.005

数学季刊 ›› 2016, Vol. 31 ›› Issue (4): 369-378.doi: 10.13371/j.cnki.chin.q.j.m.2016.04.005

一类高阶线性微分方程解的增长性

College of Mathematics and Information Science,Jiangxi Normal University

收稿日期:2014-07-08 出版日期:2016-12-30 发布日期:2020-10-30
作者简介:XIONG Hui(1989-), male, native of Nanchang, Jiangxi, M.S.D., engages in complex analysis;LIU Hui-fang(1973-), female, native of Fengcheng, Jiangxi, a professor of Jiangxi Normal University, Ph.D.,engages in complex analysis.
基金资助:
Supported by the National Natural Science Foundation of China(11201195)； Supported by the Natural Science Foundation of Jiangxi Province(20122BAB201012,20132BAB201008)；

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

College of Mathematics and Information Science,Jiangxi Normal University

Received:2014-07-08 Online:2016-12-30 Published:2020-10-30
About author:XIONG Hui(1989-), male, native of Nanchang, Jiangxi, M.S.D., engages in complex analysis;LIU Hui-fang(1973-), female, native of Fengcheng, Jiangxi, a professor of Jiangxi Normal University, Ph.D.,engages in complex analysis.
Supported by:
Supported by the National Natural Science Foundation of China(11201195)； Supported by the Natural Science Foundation of Jiangxi Province(20122BAB201012,20132BAB201008)；

摘要/Abstract

摘要： In this paper, we investigate the growth of solutions of the differential equations f^（k）+ A_k-1（z）f^（k-1）+ ··· + A₀（z）f = 0, where A_j（z）（j = 0, ···, k-1） are entire functions.When there exists some coefficient A_s（z）（s ∈ {1, ···, k-1}） being a nonzero solution of f’’+P（z）f = 0, where P（z） is a polynomial with degree n（≥ 1） and A₀（z） satisfies σ（A₀） ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.

关键词: entire function, differential equation, growth of order

Abstract: In this paper, we investigate the growth of solutions of the differential equations f^（k）+ A_k-1（z）f^（k-1）+ ··· + A₀（z）f = 0, where A_j（z）（j = 0, ···, k-1） are entire functions.When there exists some coefficient A_s（z）（s ∈ {1, ···, k-1}） being a nonzero solution of f’’+P（z）f = 0, where P（z） is a polynomial with degree n（≥ 1） and A₀（z） satisfies σ（A₀） ≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.

Key words: entire function, differential equation, growth of order

中图分类号:

O175

熊辉, 刘慧芳. 一类高阶线性微分方程解的增长性[J]. 数学季刊, 2016, 31(4): 369-378.

XIONG Hui, LIU Hui-fang. On the Growth of Solutions of a Class of Higher Order Linear Differential Equations[J]. Chinese Quarterly Journal of Mathematics, 2016, 31(4): 369-378.

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一类高阶线性微分方程解的增长性

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

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