系数是周期2πi的二阶复微分方程  

On Second Order Complex Differential Equations with Coefficients of Period 2πi

作　　者：张杰 赵东海 Zhang Jie;Zhao Donghai(School of Mathematics,China University of Mining and Technology,Jiangsu Xuzhou 221116)

机构地区：[1]中国矿业大学数学学院,江苏徐州221116

出　　处：《数学物理学报（A辑）》2023年第5期1382-1390,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11601507)。

摘　　要：该文主要通过学习了Laine的经典著作《Nevanlinna Theory and Complex Differential Equations》中关于系数A(z)是周期2πi的二阶复微分方程f"(z)+A(z)f(z)=0,λ(f)<∞的相关章节内容,发现了原来文献证明中存在的一个本质错误并给予了部分证明更正,同时也给出了一些较原文献中证明错误的结果的稍弱更正结论.This paper mainly learned classic book`Nevanlinna theory and complex differential equations'due to Laine and considered the second order complex differential equation f"(z)+A(z)f(z)=0,λ(f)<∞with coefficient A(z)whose period is 2πi.It found a possible error in the original proof and gave its partial correction,and also it gave a slightly weaker conclusion than its possibly controversial result in the original literature.

关 键 词：复微分方程 值分布 整函数 零点收敛指数 

分 类 号：O174.52[理学—数学]