Comptes Rendus
Complex analysis
Meromorphic solutions of a first order differential equations with delays
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))


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.

Revised after acceptance:
Published online:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Yu Chen and Tingbin Cao},
     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.

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