Acta mathematica scientia,Series B ›› 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
  • 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).

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

CLC Number: 

  • 30D35
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