[1]曾娟娟,刘慧芳.高阶线性微分方程亚纯解的增长性[J].江西师范大学学报(自然科学版),2016,40(03):272-275.
　ZENG Juanjuan,LIU Huifang.On the Growth of Meromorphic Solutions of Higher Order Linear Differential Equations[J].Journal of Jiangxi Normal University:Natural Science Edition,2016,40(03):272-275.
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高阶线性微分方程亚纯解的增长性()
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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:
40
期数:
2016年03期
页码:
272-275
栏目:
出版日期:
2016-07-01

文章信息/Info

Title:
On the Growth of Meromorphic Solutions of Higher Order Linear Differential Equations
作者:
曾娟娟; 刘慧芳
江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
ZENG Juanjuan; LIU Huifang
College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
微分方程;  亚纯函数;  亏值;  级;  超级
Keywords:
differential equation;  meromorphic functions;  deficient value;  order;  hyper order
分类号:
O 174.52
文献标志码:
A
摘要:
利用亚纯函数值分布理论,研究了亚纯系数高阶线性微分方程f(k)+Ak-1(z)f(k-1)+…+A0(z)f=0解的增长性,证明了如果A0(z)以∞为亏值,Aj(z)(1≤j≤k-1)满足某些条件,则上述方程的每个非零亚纯解都为无穷级,得到解的超级的下界估计.
Abstract:
The growth of solutions of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+…+A0(z)f=0 is investigated by using the value distributions theory of meromorphic functions,where Aj(z)(0≤j≤k-1) are meromorphic functions.It is shown that every nonzero meromorphic solution of such equations has infinite order,provided that A0(z) has a deficient value ∞ and Aj(z)(1≤j≤k-1) satisfying certain conditions.The lower bound of hyper order of meromorphic solutions of such equations is also estimated.

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] Hayman W.Meromorphic functions [M].Oxford:Clarendon Press,1964.
[3] Gundersen G.Finite order solutions of second order linear differential equations [J].Trans Amer Math Soc,1988,305(1):415-429.
[4] Hellerstein S,Miles J,Rossi J.On the growth of solutions of f ″+gf ’+hf=0 [J].Trans Amer Math Soc,1991,324:693-706.
[5] 陈宗煊.关于高阶线性微分方程亚纯解的增长率 [J].数学学报,1999,42(3):551-558.
[6] Wu Pengcheng,Zhu Jun.On the growth of solutions to the complex differential equation f ″+Af ’+Bf=0 [J].Science in China:Ser A,2011,54(5):939-947.
[7] 朱军,伍鹏程.关于复微分方程f ″+Af ’+Bf=0解的增长性 [J].数学年刊,2011,32A(5):531-538.
[8] 龙见仁,伍鹏程.2阶线性微分方程亚纯解的增长性 [J].山东大学学报:理学版,2012,47(8):31-33.
[9] 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.
[10] Long Jianren,Wu Pengcheng.On the hyper-order of solutions of second order linear differential equations [J].Advance in Math,2013,42(3):320-326.
[11] 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,2012,36(5):477-481.
[12] Gundersen G G.Estimates for the logarithmic derivative of a meromorphic function,plus similar estimates [J].J London Math Soc,1988,37(1):88-104.
[13] Goldberg A A,Sokolovskaya O P.Some relations for meromorphic functions of order or lower order less than one [J].Izv Vyssh Uchebn Zaved Math,1987,31(6):26-31.
[14] 陈宗煊.二阶亚纯系数微分方程亚纯解的零点 [J].数学物理学报,1996,16(3):276-283.
[15] 仪洪勋,杨重骏.亚纯函数唯一性理论 [M].北京:科学出版社,1995.

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备注/Memo

备注/Memo:
收稿日期:2015-10-20基金项目:国家自然科学基金(11201195)和江西省自然科学基金(20122BAB201012)资助项目.通信作者:刘慧芳(1973-),女,江西丰城人,教授,博士,主要从事复分析研究.
更新日期/Last Update: 1900-01-01