一类高阶线性微分方程解的增长性  

Growth of solutions to some higher-order linear differential equations

作　　者：闵小花 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：《南昌大学学报（理科版）》2014年第5期421-425,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11171170)

摘　　要：运用整函数的相关理论和亚纯函数的Nevanlinna值分布的理论和方法,研究整函数系数高阶线性微分方程解的增长性。在假设了高阶微分方程的某个系数As(z)为方程f″+P(z)f=0(其中P(z)为z的n次多项式)的一个非零解以及其它某些条件下,证明了高阶方程f(k)+Ak-1f(k-1)+…+A1f′+A0f=0的非零解均具有无穷级。It was investigated that the growth of solutions to some higher order linear differential equations by using the related theory of entire function,Nevanlinna value distribution theory and method of meromorphic function method.Let As（z）be a solution to the equation f″＋P（z）f=0,where P（z）s was a polynomial with P（z）=n,and giving other conditions on the coefficients of the higher order equation,then every nonzero solution to the equation f（k）＋Ak-1f（k-1）＋…＋A1f′＋A0f=0 satisfies p（f）=∞.

关 键 词：微分方程 整函数 增长级 

分 类 号：O174.52[理学—数学]