关于某类整函数系数高阶齐次线性微分方程解的级和零点

On the zero and hype-order of solutions of certain non-homogeneous differential equations with entire coefficients

本文研究了高阶齐次线性微分方程f(k)+Ak-1f(k-1)+…+A1f+′A0f=0的增长性问题,其中A0,A1,…,Ak-1是整函数,当存在系数为A0为缺项级数且比其它系数有较快增长的意义下时,得到了上述齐次微分方程的一定条件下超越解的超级的精确估计。

In this paper,by using the Nevanlinna value distribution theory,we investigate the growth of solutions of the differential equation,where are entire functions and the dominant coefficient has Fabry gap,We obtain general estimates of the growth and zeros of entire solutions of higher order linear differential equations.