单位圆内高阶非齐次线性微分方程解及其任意阶导数的值分布  

Value distribution of solutions of the higher-order non-homogeneous linear differential equations and their arbitrary-order derivatives in the unit disc

作　　者：龚攀[1] 钟希杰 涂金[3] GONG Pan;ZHONG Xijie;TU Jin(School of Mathematics and Computational Science,Shangrao Normal University,Shangrao 334001,China;Nanchang Jiaotong Institute,Nanchang 330100,China;School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]上饶师范学院数学与计算科学学院,江西上饶334001 [2]南昌交通学院,江西南昌330100 [3]江西师范大学数学与统计学院,江西南昌330022

出　　处：《南昌大学学报（理科版）》2024年第4期314-323,337,共11页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(12163003,12161074)。

摘　　要：研究高阶非齐次线性微分方程f^((k))+A_(k-1)(z)f^((k-1))+…+A_(1)(z)f′+A_(0)(z)f=F(z)解及其任意阶导数的值分布,其中系数是单位圆内[p,q]级有限的解析函数或者亚纯函数。得到了一些关于f^((j))(z)-φ(z)的复振荡定理,丰富和完善了前人的相关结论。In this paper,we studied the value distribution of solutions and their arbitrary-order derivatives of the higher-order non-homogeneous linear differential equation f^((k))+A_(k-1)(z)f^((k-1))+…+A_(1)(z)f′+A_(0)(z)f=F(z),where the coefficients were analytic functions or meromorphic functions of finite[p,q]-order in the unit disc.We obtained some oscillation theorems for f^((j))(z)-φ(z),which were generalizations and improvements of some previous theorems.

关 键 词：微分方程 解析函数 [p q]级 [p q]型 

分 类 号：O174.52[理学—数学]