数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (1): 355-368.doi: 10.1007/s10473-024-0119-x

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ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER*

Ziheng Feng1, Zhibo Huang1, Yezhou Li2,†   

  1. 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2. School of Science,Beijing University of Posts and Telecommunications, Beijing 100876, China
  • 收稿日期:2022-07-22 修回日期:2023-07-13 出版日期:2024-02-25 发布日期:2024-02-27
  • 通讯作者: † Yezhou Li, E-mail: yezhouli@bupt.edu.cn
  • 作者简介:Ziheng Feng, E-mail: 2020021880@m.scnu.edu.cn; Zhibo Huang, E-mail: huangzhibo@scnu.edu.cn
  • 基金资助:
    National Natural Science Foundation of China (11926201, 12171050) and the National Science Foundation of Guangdong Province (2018A030313508).

ENTIRE SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS HAVING THE SAME ORDER*

Ziheng Feng1, Zhibo Huang1, Yezhou Li2,†   

  1. 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2. School of Science,Beijing University of Posts and Telecommunications, Beijing 100876, China
  • Received:2022-07-22 Revised:2023-07-13 Online:2024-02-25 Published:2024-02-27
  • Contact: † Yezhou Li, E-mail: yezhouli@bupt.edu.cn
  • About author:Ziheng Feng, E-mail: 2020021880@m.scnu.edu.cn; Zhibo Huang, E-mail: huangzhibo@scnu.edu.cn
  • Supported by:
    National Natural Science Foundation of China (11926201, 12171050) and the National Science Foundation of Guangdong Province (2018A030313508).

摘要: In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.

关键词: entire solutions, radial order, Julia limiting direction, Baker wandering domain, transcendental direction

Abstract: In this paper, we consider entire solutions of higher order homogeneous differential equations with the entire coefficients having the same order, and prove that the entire solutions are of infinite lower order. The properties on the radial distribution, the limit direction of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.

Key words: entire solutions, radial order, Julia limiting direction, Baker wandering domain, transcendental direction

中图分类号: 

  • 30D35