Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (1): 439-449.doi: 10.1007/s10473-023-0124-5

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THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS*

Zhibo Huang, Minwei Luo, Zongxuan Chen   

  1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2021-04-22 Revised:2022-06-11 Published:2023-03-01
  • Contact: †Zhibo HUANG. E-mail:huangzhibo@scnu.edu.cn
  • About author:Minwei Luo,E-mail: 2019021673@m.scnu.edu.cn; Zongxuan Chen,E-mail:chzx@vip.sina.com
  • Supported by:
    *National Natural Science Foundation of China (12171050, 11871260) and National Science Foundation of Guangdong Province (2018A030313508)

Abstract: By looking at the situation when the coefficients $P_{j}(z)$ $(j=1,2,\cdots,n-1)$ (or most of them) are exponential polynomials, we investigate the fact that all nontrivial solutions to higher order differential equations $f^{(n)}+P_{n-1}(z)f^{(n-1)}+\cdots+P_{0}(z)f=0$ are of infinite order. An exponential polynomial coefficient plays a key role in these results.

Key words: differential equations, entire solution, exponential polynomial, growth

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