关于高阶线性微分方程解的零点

ZEROS OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

本文研究了k(≥2)阶齐次线性微分方程(其中P1(z)=ξ1zn+…,P2(z)=ξ2zn+…为非常数多项式. Q1(z)(≠0),Q2(z)(≠0),Q(z),aj(z)(j=1,2,…,k一1)均为级小于n的整函数)的非平凡解f的复振荡问题,得出当ξ2-ξ1为正实数时,方程解的零点序列收敛指数的一些结果.

In this paper, we study the zeros of the solution of higher order defferential equation: where P1(z) = 1zn +…,P2(z) = 2zn +… are non-constant polynomials, and Q1(z)( 0), Q2(z)( 0), Q(z), aj(z)(j = 1, 2,…, k - 1) are entire functions and their orders are less than n .We obtain some results which generalize a theorem given by K. Ishizaki.