一类高阶齐次线性微分方程解的复振荡

Complex Oscilition of the Solutions of a Type of Higher Order Linear Differential Equations

研究了高阶齐次线性微分方程f(k)+(Ak-1(z)epk-1(z)+Dk-1(z))f(k-1)+…+(A0(z)ep0(z)+D0(z))f=0解的增长性问题,其中pj(z)=ajzn+bj,1zn-1+…+bjn,,Aj(z),Dj(z)是有限级整函数。针对pj(z)中aj(j=0,1,…,k-1)的幅角主值不全相等的情形,得到了方程解的增长级的精确估计。

This paper investigates the properties of growth of solutions of higher order Linear Differential equations f（k）＋（A^k-1（z）e^pk-1（z）＋Dk-1（z））f（k-1）＋L＋（A0（z）e^po（z）＋D0（z））f =0, in the pj（z）=aj zn＋bj,1zn-1＋bj,n,Aj（z） and Dj（z） were finite order entire function,obtains some precise estimates of the order of growth of the solutions when argument of pj（z）中aj（j=0,1,L,k-1） of pj（z） is not all equal.