某类高阶整函数系数微分方程解的零点和超级

On the Zero and Hype-order of Solutions of Certain Non-homogeneous Differential Equations with Entire Coefficients

研究了非齐次线性微分方程f(k)+Ak-1fk-1+…+Asf(s)+…+A0f=F的增长性问题,其中A0,A1,…,Ak-1,F是整函数,当存在某个系数As(s∈{0,1,…,k-1})为缺项级数且比其它系数有较快增长的意义下时,得到了上述非齐次微分方程的一定条件下超越解的超级的精确估计。

By using the Nevanlinna Value distribution theory, the paper investigates the growth of solutions of the differential equation f^（k）＋Ak-1 f^k-1＋…＋Af^（s）＋…＋A0f=F,where A0,A1,…,Ak-1, F are entire functions and the dominant coeffcient As has fabry gap,it obtaines general estimates of the growth and zeros of entire solutions of higher order linear differential equations.