某类高阶复微分方程解的增长性

The Growth of Solutions of a Class of Higher Order Complex Differential Equations

主要研究高阶微分方程f(k)+∑k-1j=1Pj(e-z)f(j)+Q(z)f=0解的增长性,其中Q(z)是有限级超越整函数,Pj(e-z)(j=1,2,…,k-1)为e-z的非常数多项式.当Q(z)满足一定条件时,该微分方程的任意非平凡解为无穷级解,并讨论了对应的非齐次微分方程解的增长性.

The growth of solutions of the higher order linear differential equations f（ k）＋ ∑j = 1Pj（ e-z） f（ j）＋ Q（ z） f =0 are discussed,where Q（ z） is a transcendental entire function of finite order,and Pj（ e- z） are non-constant polynomials. Some conditions on Q（ z） are given which can guarantee that every non-rivial solution of the equation is infinite order,the growth of solutions to the corresponding non-homogeneous differential equation is discussed.