摘要
研究整函数系数高阶线性微分方程f^((k))+A_(k-1)f^((k-1))+…+A_0f=0解的增长性.利用亚纯函数的Nevanlina值分布理论,得到当系数A_s(s≠0)为满足杨不等式极端情况的整函数,A_0满足一定条件时,上述方程的每个非零解均为无穷级,并给出解的超级估计.
In this paper,we investigate the growth of solutions of higher order linear differential equation F^(k) + A(k-1)f^(k-1)+…+A0f = 0 with entire coefficients.By using the Nevanlinna' s value distribution theory,and assume that AS(s≠0) is extremal for Yang's inequality,we obtain that every nontrivial solution of the above equation is of infinite order under some conditions on A0.We also obtain the estimate on the hyper-order of its solutions.
作者
袁蓉
刘慧芳
YUAN Rong LIU Hui-fang(College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 33002)
出处
《数学的实践与认识》
北大核心
2017年第2期243-249,共7页
Mathematics in Practice and Theory
基金
国家自然科学基金(11661044
11201195)
江西省自然科学基金(20132BAB201008)
关键词
整函数
杨不等式
微分方程
增长级
entire function
Yang's inequality
differential equation
growh of order