某类系数与Fejér缺项级数有关的齐次和非齐次高阶线性微分方程亚纯解的增长性  

Growth of Meromorphic Solutions of Some Kind of Homogeneous and Non-homogeneous Higher Order Linear Differential Equations with Coefficients Relative to Fejér Gap Series

作　　者：周艳萍[1] 郑秀敏[1] ZHOU Yan-ping;ZHENG Xiu-min(Institute of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022)

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022

出　　处：《工程数学学报》2018年第5期545-558,共14页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11761035);江西省自然科学基金(20171BAB201002).

摘　　要：Nevanlinna理论在复微分方程领域中具有广泛的应用,其中运用该理论研究复线性微分方程亚纯解的增长性和值分布与系数的增长性之间的关系是复微分方程领域中的重要论题.由于缺项级数具有一些特殊性质,当缺项级数作为方程系数时,这些性质即可发挥作用.因此,我们可结合缺项级数的定义和性质研究复线性微分方程亚纯解的性质.在本文中,我们运用Nevanlinna理论并结合Feér缺项级数的定义和性质对一类齐次和非齐次高阶复线性微分方程进行了研究.当方程的某个系数与Fejér缺项级数有关而其余系数为整函数或亚纯函数时,得到了方程亚纯解的增长级的估计,推广并改进了前人已有结果.Nevanlinna theory has been widely applied in the field of complex differential equations.It is an important research subject to explore the relationship between the growth of the coefficients and the growth and value distribution of meromorphic solutions of complex linear differential equations by Nevanlinna theory.Meanwhile,the gap series has some special properties which may play important roles when the gap series appear as the coefficients of certain equation.Therefore,the properties of meromorphic solutions of complex linear differential equations can be investigated by combining with the definition and properties of gap series.In this paper,we consider a kind of the homogeneous and non-homogeneous higher order complex linear differential equation based on Nevanlinna theory and the definition and properties of Fej′er gap series.When one of the coefficients is relative to Fej′er gap series and the others are entire or meromorphic functions,the estimates on the order of meromorphic solutions of the involved equation are obtained,which promotes and improves the previous research results.

关 键 词：复线性微分方程 NEVANLINNA理论 Fejer缺项级数 迭代级 迭代型 

分 类 号：O174.52[理学—数学]