复合函数-微分方程亚纯解的性质

数学物理学报 ›› 2020, Vol. 40 ›› Issue (5): 1121-1131.

• 论文 • 下一篇

复合函数-微分方程亚纯解的性质

刘曼莉¹(),高凌云^2,*()

¹ 山东大学数学学院济南 250100
² 暨南大学数学系广州 510632

收稿日期:2020-01-19 出版日期:2020-10-26 发布日期:2020-11-04
通讯作者: 高凌云 E-mail:lml6641@163.com;tgaoly@jnu.edu.cn
作者简介:刘曼莉, E-mail:lml6641@163.com
基金资助:
山东省自然科学基金(ZR2018MA014)

Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations

Manli Liu¹(),Lingyun Gao^2,*()

¹ School of Mathematics, Shandong University, Jinan 250100
² Department of Mathematics, Jinan University, Guangzhou 510632

Received:2020-01-19 Online:2020-10-26 Published:2020-11-04
Contact: Lingyun Gao E-mail:lml6641@163.com;tgaoly@jnu.edu.cn
Supported by:
the NSF of Shandong Province(ZR2018MA014)

摘要/Abstract

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）=awⁿ⁺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.

关键词: 亚纯函数, 复合函数-微分方程, 增长级, Nevanlinna值分布理论

Abstract:

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⁾=awⁿ⁺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.

Key words: Meromorphic solutions, Complex functional differential equations, Growth order, Nevanlinna theory

中图分类号:

O174

刘曼莉,高凌云. 复合函数-微分方程亚纯解的性质[J]. 数学物理学报, 2020, 40(5): 1121-1131.

Manli Liu,Lingyun Gao. Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations[J]. Acta mathematica scientia,Series A, 2020, 40(5): 1121-1131.

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复合函数-微分方程亚纯解的性质

Behaviour of Meromorphic Solutions of Complex Functional-Differential Equations

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