一类高阶线性微分方程解的增长性  

On the Growth of Solutions of Certain Higher Order Linear Differential Equation

作　　者：袁蓉[1] 刘慧芳[1] YUAN Rong LIU Hui-fang(College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 33002)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《数学的实践与认识》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)

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.

关 键 词：整函数 杨不等式 微分方程 增长级 

分 类 号：O174.52[理学—数学] O175[理学—基础数学]