Comptes Rendus
Analyse complexe
Meromorphic solutions of a first order differential equations with delays
Yu Chen1 ; Tingbin Cao1  
1 Department of Mathematics, Nanchang University, Nanchang city, Jiangxi 330031, P. R. China
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 665-678.

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)w ′ (z) w(z) k =R(z,w(z))

and

w(z+1)+a(z)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.

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DOI : 10.5802/crmath.331
Classification : 34K40, 30D35, 34M55
Yu Chen 1 ; Tingbin Cao 1

1 Department of Mathematics, Nanchang University, Nanchang city, Jiangxi 330031, P. R. China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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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