[1]谭 晖,肖丽鹏*.关于一类高阶复微分方程解的增长性[J].江西师范大学学报(自然科学版),2022,(04):335-341.[doi:10.16357/j.cnki.issn1000-5862.2022.04.02]
 TAN Hui,XIAO Lipeng*.On the Growth of Solutions of a Class of Higher Order Complex Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2022,(04):335-341.[doi:10.16357/j.cnki.issn1000-5862.2022.04.02]
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关于一类高阶复微分方程解的增长性()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2022年04期
页码:
335-341
栏目:
复分析
出版日期:
2022-07-25

文章信息/Info

Title:
On the Growth of Solutions of a Class of Higher Order Complex Differential Equations
文章编号:
1000-5862(2022)04-0335-07
作者:
谭 晖肖丽鹏*
江西师范大学数学与统计学院,江西 南昌 330022
Author(s):
TAN HuiXIAO Lipeng*
School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
高阶线性微分方程 整函数 增长级 超级
Keywords:
higher order linear differential equation entire function the growth order hyper-order
分类号:
O 174.52
DOI:
10.16357/j.cnki.issn1000-5862.2022.04.02
文献标志码:
A
摘要:
该文研究了一类高阶线性微分方程f (k)+Ak-1 f (k-1)+…+A1 f '+A0 f=F(z)解的增长性,其中A0,A1,…,Ak-1,F(z)是整函数,并且A0、A1是另一个2阶线性方程的非平凡解. 推广了龙见仁等得到的结果.
Abstract:
In this paper,the growth of solutions of a class of higher order linear differential equations f (k)+Ak-1 ·f k-1+…+A1 f '+A0 f=F(z) is studied,where A0,A1,…,Ak-1,F(z) are entire functions,in addition,A0 and A1 are non-trivial solutions of another second-order linear equation.Previous results which are obtained by Long Jianren,Wu Tingmi and Wu Xiubi are promoted.

参考文献/References:

[1] 杨乐.值分布论及其新研究[M].北京:科学出版社,1982.
[2] LAINE I.Nevanlinna theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[3] HAYMAN W K.Meromorphic function[M].Oxford:Clarendon Press,1964.
[4] 仪洪勋,杨重骏.亚纯函数唯一性理论[M].北京:科学出版社,1995.
[5] LONG Jianren,WU Pengcheng,WU Xiubi.On the zero distribution of solutions of second order linear differential equations in the complex domain[J].New Zealand Journal of Mathematics,2012,42:9-16.
[6] GUNDERSEN G G.On the real zeros of solutions of f ″+A(z)f=0 where A(z) is entire[J].Annals Academiae Scientiarum Fennicae:Mathematica,1986,11:275-294.
[7] GUNDERSEN G G.Finite order solutions of second order linear differential equations[J].Transactions of the American Mathematical Society,1988,305(1):415-429.
[8] HELLERSTEIN S,MILES J,ROSSI J.On the growth of solutions of f ″+gf'+hf=0[J].Transactions of the American Mathematical Society,1991,324(2):693-706.
[9] LONG Jianren,WU Tingmi,WU Xiubi.Growth of solutions of complex differential equations with solutions of another equation as coefficients[J].Computational Methods and Function Theory,2019,19(1):3-16.
[10] 高仕安,陈宗煊,陈特为.线性微分方程的复振荡理论[M].武汉:华中理工大学出版社,1998.
[11] GUNDERSEN G G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates[J].Journal of the London Mathematical Society,1988,37(1):88-104.
[12] CHEN Zongxuan,SHON K H.On the growth of solutions of a class of higher order differential equations[J].Acta Mathematica Scientia,2004,24B(1):52-60.

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备注/Memo

备注/Memo:
收稿日期:2021-10-20
基金项目:国家自然科学基金(11661043)资助项目.
通信作者:肖丽鹏(1979—),女,江西吉安人,副教授,博士,主要从事复分析研究.E-mail:2992507211@qq.com
更新日期/Last Update: 2022-07-25