一类亚纯系数高阶线性微分方程解的增长性  

The Growth for Solutions of a Class of Higher Order Linear Differential Equations with Meromorphic Coefficients

作　　者：艾丽娟[1] 易才凤[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2014年第3期250-253,260,共5页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11171170)资助项目

摘　　要：运用Nevanlinna值分布的理论和方法,研究了微分方程f(k)+Ak-1f(k-1)+…+A1f'+A0f=0(k≥2)解的增长性,其中Aj(j=0,1,…,k-1)是亚纯函数,通过给定Aj的不同条件,证明了齐次线性微分方程的任一非零解均为无穷级.The growth of solutions of the differential equation f（k）＋…＋A0f =0（k≥2）is investigated by using the fundamental theory of Nevanlinna value distribution,where Aj（0 ≤ j ≤ k - 1）are meromorphic functions. It is proved that every nontrivial solution f of the equation is of infinite order with giving some different condition on Aj （0≤j≤k -1）.

关 键 词：微分方程 亚纯函数 亏值 无穷级 

分 类 号：O174.52[理学—数学]