Meromorphic solutions of a first order differential equations with delays

Yu Chen; Tingbin Cao

doi:10.5802/crmath.331

Complex analysis

Meromorphic solutions of a first order differential equations with delays

Yu Chen ¹; Tingbin Cao ¹

¹ Department of Mathematics, Nanchang University, Nanchang city, Jiangxi 330031, P. R. China

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 665-678.

Abstract

The main purpose of this paper is to study meromorphic solutions of the first order differential equations with delays

w (z + 1) - w (z - 1) + a (z) {(\frac{w^{'} (z)}{w (z)})}^{k} = R (z, w (z))

and

w (z + 1) + a (z) {(\frac{w^{'} (z)}{w (z)})}^{k} = R (z, w (z)),

where $k$ is a positive integer, $a (z)$ is a rational function, $R (z, w)$ is rational in $w$ with rational coefficients. Some necessary conditions on the degree of $R (z, w)$ are obtained for the equation to admit a transcendental meromorphic solution of minimal hypertype. These are extensions of some previous results due to Halburd, Korhonen, Liu and others. Some examples are given to support our conclusions.

Received: 2021-09-29
Accepted: 2022-01-17
Revised after acceptance: 2022-01-24
Published online: 2022-06-22

Zbl

DOI: 10.5802/crmath.331

Classification: 34K40, 30D35, 34M55

Author's affiliations:

Yu Chen ¹; Tingbin Cao ¹

¹ Department of Mathematics, Nanchang University, Nanchang city, Jiangxi 330031, P. R. China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Meromorphic solutions of a first order differential equations with delays},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {665--678},
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Yu Chen; Tingbin Cao. Meromorphic solutions of a first order differential equations with delays. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 665-678. doi : 10.5802/crmath.331. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.331/

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