一类线性微分方程解复振荡结果的综述

A Summary of the Result of Complex Oscillation of a Kind of Linear Differential Equation

本文讨论二阶方程∫′+(R_1(Z)e^P1^(z)+R_2(Z)e^P2~2+Q(Z)f=0,(其中P_1(Z)=ζ_1Z^n+……,P_2(Z)=ζ_2Z^n为非常数多项式.R_1(Z)≡0,R_2(Z)?0,Q(Z)为级小于n的整函数)在ζ_1/ζ_2的条件下,任一非平凡解的零点收敛指数.

This paper discusses, under the condition of ζ_1/ζ_2, the convergent exponent of the zero sequenceof the second order equation f' + R_1 (z) e^(P_1(z)) + R_2(z) e^(P_2(z)) + Q(z)f = 0, in which P_1 (z)=ζ_1, z^n + ……, P_2(z) = ζ_2z^n are nonconsonant polynomial, R_1 (z) 0, R_2(z) 0,Q(Z) is entire function whose series is less than n.