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. 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 Gao2,*()   

  1. 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:

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')nwn=awn+1g)+bw+d

亚纯解的存在性问题,得到了当a≠0,bd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