某类高阶复微分方程解的增长性

主要研究高阶微分方程 f（k）+∑k-1 j =1 Pj（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 a Class of Higher Order Complex Differential Equations

The growth of solutions of the higher order linear differential equations f(k)+∑k-1j=1 Pj(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 polyno-mials. Some conditions on Q( z)are given which can guarantee that every non-rivial solution of the equation is infi-nite order,the growth of solutions to the corresponding non-homogeneous differential equation is discussed.