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 Coefficient

作　　者：杨碧珑[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）》2012年第5期477-481,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)1Ak-1f(k-1)+…+A1f'+Af=0(k≥2)解的增长性,其中Aj(1≤j≤K-1),A为亚纯函数,假设A是以∞为亏值的超越亚纯函数,通过给定Aj(1≤j≤k-1)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）1Ak-1f（k-1）＋…＋A1f＇＋Af=0（k≥2） is investigated by using the fundamental theory and method of Nevanlinna,where Aj（1≤j≤K-1）and A■0 are meromorphic functions.Assuming that A is transcendental and A has a deficient value ∞,it is proved that every solution f■0 of the equation is of infinite order with giving some different condition on Aj（1≤j≤K-1）.

关 键 词：微分方程 亚纯函数 亏值 级 

分 类 号：O174.52[理学—数学]