摘要
运用Nevanlinna值分布的理论和方法,首先研究了二阶微分方程f″+A(z)f′+B(z)f=0解的增长性,其中A(z)是具有有穷亏值的有限级亚纯函数,对B(z)给出适当的条件,证明了方程的每一个非零解具有无穷级;然后研究了一类高阶非齐次线性微分方程解的振荡性质,得到了其解的超级及二级零点收敛指数的精确估计。
First,the growth of solutions of the differential equation f″＋A（z）f′＋B（z）f=0is investigated by using the fundamental theory and method of nevanlinna,where A（z）is a finite order meromorphic function with a finite deficient value.It is proved that every nontrivial solution fof the equation is of infinite order with giving some different condition on B（z）.Then the precise estimates of the hyper-order of solutions to the nonhomogeneous higher order linear differential equation are obtained.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第6期14-18,共5页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金(11171170)
关键词
微分方程
亚纯函数
整函数
亏值
无穷级
differential equation
meromorphic functions
entire functions
deficient value
infinite order
