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

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）.