[1]艾丽娟,易才凤.一类亚纯系数高阶线性微分方程解的增长性[J].江西师范大学学报(自然科学版),2014,(03):250-253.
 AI Li-juan,YI Cai-feng.The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients[J].,2014,(03):250-253.
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一类亚纯系数高阶线性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:
2014年03期
页码:
250-253
栏目:
出版日期:
2014-06-30

文章信息/Info

Title:
The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients
作者:
艾丽娟;易才凤
江西师范大学数学与信息科学学院,江西 南昌,330022
Author(s):
AI Li-juan;YI Cai-feng
关键词:
微分方程亚纯函数亏值无穷级
Keywords:
differential equationmeromorphic functiondeficient valueinfinite order
分类号:
O174.52
文献标志码:
A
摘要:
运用Nevanlinna值分布的理论和方法,研究了微分方程f(k)+Ak-1 f(k-1)+…+A1 f ′+A0 f=0( k≥2)解的增长性,其中Aj(j=0,1,…,k-1)是亚纯函数,通过给定Aj 的不同条件,证明了齐次线性微分方程的任一非零解均为无穷级。
Abstract:
The growth of solutions of the differential equation f(k)+…+A0f =0(k≥2)is investigated by using the fundamental theory of Nevanlinna value distribution,where Aj(0 ≤ j ≤ k - 1)are meromorphic functions. It is proved that every nontrivial solution f of the equation is of infinite order with giving some different condition on Aj (0≤j≤k -1).

参考文献/References:

[1] Hayman W.Meromorphic function [M].Oxford:Clarendon Press,1964.
[2] 杨乐.值分布论及其新研究 [M].北京:科学出版社.1982.
[3] Chen Zongxuan,Gao Shian.Some oscillation theorems of higher order non-homogeneous linear differential equations with transcendental meromorphic coefficents [J].Ann of diff Eqs,1996,12:28-39.
[4] 龙见仁,朱军,李晓曼.一类高阶线性微分方程解的增长性 [J].数学物理学报.2013,33A(3):401-408.
[5] 朱军,伍鹏程.关于复微分方程f ″+Af '+Bf=0解的增长性(2) [J].数学年刊.2011,32 A(5):531-538.
[6] 刘旭强,易才凤.关于2阶线性微分方程f ″+Af '+Bf=0解的增长性 [J].江西师范大学学报:自然科学版,2013,37(2):171-174.
[7] 杨碧珑,易才凤.一类亚纯系数高阶线性微分方程解的增长性 [J].江西师范大学学报:自然科学版,2012,36(5):477-481.
[8] Gundersen G G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates [J].J London Math Soc,1988,37(2):88-104.
[9] Fuchs W.Proof of a conjectrue of G Polya concerning gaps series [J].Illinois J Math,1963,7:661-667.
[10] Hellenstein S,Miles J,Rossi J.On the growth of solutions of certain linear differential equations [J].Ann Acad Sci Fenn Ser A I Math,1992,17:343-365.
[11] Zhu Jun,Wu Pengcheng.On the growth of solutions of the complex differential equationf ″+Af '+Bf=0 [J].Science in China Ser A,2011,54(5):939-947.

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备注/Memo

备注/Memo:
国家自然科学基金(11171170)
更新日期/Last Update: 1900-01-01