高阶线性微分方程解的角域增长性

GROWTH OF THE SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS IN AN ANGLE

假设A_0,A_1,…,A_(k-1)在某个角域内解析,讨论高阶线性微分方程f^(k)+A_(k-1)f^((k-1))+…+A_1f′+A_0f=0在特定角域内解的增长性和渐近性,改进了一些结果.

The higher order linear differential equation f^（k） ＋ A^k-1f^（k-1） ＋… ＋ A1f′ ＋ A0f = 0 is considered, where A0, A1,…, Ak-1 are analytic in an angle, and the growth and asymptotic character of solutions of the equation restricted in the angle are obtained. Some existing results are improved.