复合函数-微分方程亚纯解的性质  

Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations

作　　者：刘曼莉 高凌云[2] Liu Manli;Gao Lingyun(School of Mathematics,Shandong University,Jinan 250100;Department of Mathematics,Jinan University,Guangzhou 510632)

机构地区：[1]山东大学数学学院,济南250100 [2]暨南大学数学系,广州510632

出　　处：《数学物理学报（A辑）》2020年第5期1121-1131,共11页Acta Mathematica Scientia

基　　金：山东省自然科学基金(ZR2018MA014)。

摘　　要：该文致力于研究两个问题.首先,考虑了如下一类复合函数-微分方程(w')^nw^(n)=aw^n+1(g)+bw+d亚纯解的存在性问题,得到了当a≠0,b,d是复常数且w是一个超越亚纯函数时,则g必为线性的.其次,鉴于方程和方程组之间的本质区别,研究复合函数方程组是有意义的.该文也考虑了一类复合函数方程组,在适当限制条件下,得到了其亚纯解的存在形式.有例子表明文中的结论是成立的.The aim of this paper is twofold.Firstly,we consider the existence of solutions to a type of complex functional-differential equations(w')^nw^(n)=aw^n+1(g)+bw+d in complex variables.We obtain g is linear when w is a transcendental meromorphic function and a≠0,b,d are constants.In addition,due to the different properties between equations and system of equations,it is meaningful to research systems of equations,this paper is also concerned with a type of system of functional equations,properties of meromorphic solutions are obtained under some proper conditions.Examples are constructed to show that our results are accurate.

关 键 词：亚纯函数 复合函数-微分方程 增长级 NEVANLINNA值分布理论 

分 类 号：O174[理学—数学]