[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].,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 JuanjuanLIU 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 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.

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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