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The main purpose of this paper is to study meromorphic solutions of the first order differential equations with delays
and
where is a positive integer, is a rational function, is rational in with rational coefficients. Some necessary conditions on the degree of 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.
Chen, Yu 1 ; Cao, Tingbin 1
@article{CRMATH_2022__360_G6_665_0, author = {Chen, Yu and Cao, Tingbin}, title = {Meromorphic solutions of a first order differential equations with delays}, journal = {Comptes Rendus. Math\'ematique}, pages = {665--678}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, number = {G6}, year = {2022}, doi = {10.5802/crmath.331}, zbl = {07547265}, language = {en}, url = {http://geodesic.mathdoc.fr/articles/10.5802/crmath.331/} }
TY - JOUR AU - Chen, Yu AU - Cao, Tingbin TI - Meromorphic solutions of a first order differential equations with delays JO - Comptes Rendus. Mathématique PY - 2022 SP - 665 EP - 678 VL - 360 IS - G6 PB - Académie des sciences, Paris UR - http://geodesic.mathdoc.fr/articles/10.5802/crmath.331/ DO - 10.5802/crmath.331 LA - en ID - CRMATH_2022__360_G6_665_0 ER -
%0 Journal Article %A Chen, Yu %A Cao, Tingbin %T Meromorphic solutions of a first order differential equations with delays %J Comptes Rendus. Mathématique %D 2022 %P 665-678 %V 360 %N G6 %I Académie des sciences, Paris %U http://geodesic.mathdoc.fr/articles/10.5802/crmath.331/ %R 10.5802/crmath.331 %G en %F CRMATH_2022__360_G6_665_0
Chen, Yu; Cao, Tingbin. Meromorphic solutions of a first order differential equations with delays. Comptes Rendus. Mathématique, Tome 360 (2022) no. G6, pp. 665-678. doi : 10.5802/crmath.331. http://geodesic.mathdoc.fr/articles/10.5802/crmath.331/
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