一类高阶齐次线性微分方程解的零点

ZEROS OF SOLUTIONS OF CERTAIN HIGHER ORDER HOMOGENEOUS LINEAR DIFFERENTIAL EQUATIONS

本文研究一类整函数系数高阶齐次线性微分方程解的零点分布.利用Nevanlinna值分布理论,得到当系数A_(k-1)的增长性起主要支配作用时,方程f^((k))+A_(k-1)f^((k-1))+···+A_0f=0任意超越解的零点收敛指数为无穷,推广了Langley和Bank等人的结果.

In this paper,we investigate the distribution of the zeros of the solutions for certain higher order homogeneous linear differential equations f（k）＋ A_（k-1）f（k-1）＋ · · · ＋ A_0 f = 0with entire coefficients.By using the Nevanlinna＇s value distribution theory,we obtain that the exponent of convergence of zeros of every transcendental solution is infinite when A_（k-1）is the dominant coefficient,which extends the results of Langley and Bank.