摘要
首先研究了与Saxer-Millioux定理相关的复微分方程,并运用多复变对数导数引理将该结果推广至关于整函数全导数的微分多项式;其次利用Clunie的结果将Hayman的定理推广至多复变整函数的全导数情形;最后作为推论得到一些多复变Picard型定理.
In this paper,we study complex differential equations related to the Picard type theorem of Saxer-Millioux,and use the logarithmic derivative lemma for several complex variables to extend the result to differential polynomials of entire functions.By using Clunie′s results,Hayman′s theorem is extended to total derivative of entire functions in several complex variables.As corollaries,we obtain some Picard type theorems and their higher dimensional extensions.
作者
李菲
杨刘
LI Fei;YANG Liu(School of Mathematics and Physics,Anhui University of Technology,Maanshan 243032,China)
出处
《纯粹数学与应用数学》
2023年第1期145-158,共14页
Pure and Applied Mathematics
基金
国家自然科学基金(11701006)
安徽省高等学校科学研究项目(2022AH050329,2022AH050290).
关键词
微分方程
整函数
全导数
Picard型定理
differential equation
entire function
total derivative
theorems of Picard type