奇点附近高阶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 Homogeneous Linear Differential Equations and Their Arbitrary-order Derivatives Near a Singular Point

作　　者：龚攀 涂金[2] 徐洪焱 GONG Pan;TU Jin;XU Hongyan(School of Mathematics and Computer Science,Shangrao Normal University,Shangrao 334001,China;School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China;College of Arts and Sciences,Suqian University,Suqian 223800,China)

机构地区：[1]上饶师范学院数学与计算机科学学院,江西上饶334001 [2]江西师范大学数学与统计学院,江西南昌330022 [3]宿迁学院文理学院,江苏宿迁223800

出　　处：《应用数学》2024年第3期618-628,共11页Mathematica Applicata

基　　金：国家自然科学基金(12161074,12163003)。

摘　　要：本文研究高阶齐次线性微分方程解及其任意阶导数的值分布,其中系数在奇异点附近解析或者亚纯.得到该方程解的增长性的一些估计,并推广和改进了相关定理.In this paper,we study the value distribution of solutions and their arbitrary-order derivatives of the higher-order homogeneous linear differential equation,where the coefficients are analytic or meromorphic in near a singular point.Some estimations of the growth of solutions of the equation are obtained,which are generalizations and improvements of some previous theorems.

关 键 词：奇点 迭代级 小函数 解析函数 

分 类 号：O174.52[理学—数学]