线性微分方程无穷下级整函数解的Baker游荡域  

Baker Wandering Domain of Entire Solutions with Infinite Lower Order for Linear Differential Equations

作　　者：张希 龙芳 王珺[1] ZHANG Xi;LONG Fang;WANG Jun(School of Mathematical Sciences,Fudan University,Shanghai 200433,China;Department of Basic Courses,Jiangxi Province Machinery Senior Technician School,Nanchang,Jiangxi 330013,China)

机构地区：[1]复旦大学数学科学学院,上海200433 [2]江西省机械高级技工学校基础课部,江西南昌330013

出　　处：《复旦学报（自然科学版）》2024年第4期438-442,共5页Journal of Fudan University：Natural Science

基　　金：国家重点研发计划“数学和应用研究”重点专项(2021YFA1003200)。

摘　　要：利用Nevanlinna理论和复方程中的比较定理研究了线性微分方程。当方程系数和非齐次项具有公共的非超越方向时,无穷下级的整函数解及其任意阶导数、原函数均没有Baker游荡域。此外,当方程系数有公共的非超越方向且非齐次项的级有穷时,结论依然成立。The Baker wandering domains of entire solutions for general linear differential equations are studied by using the Nevanlinna theory and the comparison theorem in differential equations.When the coefficients and the non-homogeneous term of the equations have common non-transcendental directions,there is no Baker wandering domain for the entire solutions with infinite lower order.In addition,the conclusion still holds when the coefficients have common non-transcendental directions and the non-homogeneous term is of finite order.

关 键 词：线性微分方程 整函数 Baker游荡域 超越方向 

分 类 号：O174.52[理学—数学]