Analyse complexe

Meromorphic solutions of a first order differential equations with delays

Chen, Yu¹ ; Cao, Tingbin¹  

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

Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 665-678.

Résumé

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

$$w(z+1)-w(z-1)+a\left(z\right){\left(\frac{w^{\prime }\left(z\right)}{w\left(z\right)}\right)}^k=R(z,w\left(z\right))$$

and

$$w(z+1)+a\left(z\right){\left(\frac{w^{\prime }\left(z\right)}{w\left(z\right)}\right)}^k=R(z,w\left(z\right)),$$

where $k$ is a positive integer, $a\left(z\right)$ 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.

Détail

Reçu le : 2021-09-29
Accepté le : 2022-01-17
Accepté après révision le : 2022-01-24
Publié le : 2022-06-22
DOI : 10.5802/crmath.331

Classification : 34K40, 30D35, 34M55

Licence : CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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