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

doi:10.1007/s10473-023-0124-5

数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (1): 439-449.doi: 10.1007/s10473-023-0124-5

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

Zhibo Huang^†, Minwei Luo, Zongxuan Chen

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

收稿日期:2021-04-22 修回日期:2022-06-11 发布日期:2023-03-01
通讯作者: †Zhibo HUANG. E-mail:huangzhibo@scnu.edu.cn
基金资助:
*National Natural Science Foundation of China (12171050, 11871260) and National Science Foundation of Guangdong Province (2018A030313508)

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

Zhibo Huang^†, Minwei Luo, Zongxuan Chen

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)

摘要/Abstract

摘要： 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.

关键词: differential equations, entire solution, exponential polynomial, growth

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

Zhibo Huang, Minwei Luo, Zongxuan Chen. THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS^*[J]. 数学物理学报(英文版), 2023, 43(1): 439-449.

Zhibo Huang, Minwei Luo, Zongxuan Chen. THE GROWTH OF SOLUTIONS TO HIGHER ORDER DIFFERENTIAL EQUATIONS WITH EXPONENTIAL POLYNOMIALS AS ITS COEFFICIENTS^*[J]. Acta mathematica scientia,Series B, 2023, 43(1): 439-449.

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

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

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