[1]涂鸿强,刘慧芳.一类2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),2017,(02):184-188.
 TU Hongqiang,LIU Huifang.On Growth of Solutions of Some Second Order Linear Differential Equations[J].,2017,(02):184-188.
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一类2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:
2017年02期
页码:
184-188
栏目:
出版日期:
2017-03-01

文章信息/Info

Title:
On Growth of Solutions of Some Second Order Linear Differential Equations
作者:
涂鸿强刘慧芳
江西师范大学数学与信息科学学院,江西 南昌 330022
Author(s):
TU HongqiangLIU Huifang
College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China
关键词:
微分方程 整函数 Denjoy猜想 增长级
Keywords:
differential equation entire function Denjoy’s conjecture order of growth
分类号:
O 174.52
文献标志码:
A
摘要:
研究2阶微分方程f ″+A1(z)f ’+A0(z)f=0解的增长性.假设A1(z)=h1eQ1(z)+h2eQ2(z),其中Qj(j=1,2)n(n≥1)次多项式,hj(j=1,2)为级小于n的整函数,A0为满足下级μ(A0)≠n的超越整函数或A0为满足Denjoy猜想极值情况的整函数,得到上述方程的每个非零解都具有无穷级,同时对解的超级进行了估计.
Abstract:
The growth of solutions of second order linear differential equations f ″+A1(z)f ’+A0(z)f=0 is investigated.Let A1(z)=h1eQ1(z)+h2eQ2(z),where Qj(z)(j=1,2) are polynomials with degree n(n≥1),hj(j=1,2) are entire functions with order less than n,and let A0 be a transcendental entire function with lower order μ(A0)≠n or A0 or a function extremal for Denjoy’s conjecture,then every nontrivial solution of such equations is of infinite order.Some estimates on hyper-order of its solutions are also obtained.

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备注/Memo

备注/Memo:
收稿日期:2016-10-10基金项目:国家自然科学基金(11661044)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.E-mail:liuhuifang73@sina.com
更新日期/Last Update: 1900-01-01