Zeros of the Solutions of First Order Functional Differential Equations

Abstract

It is shown that all solutions of a class of first order autonomous functional differential equations are oscillatory if the fundamental solution has a first zero $T_1 $. If the fundamental solution does not have any zeros, we show that every solution with positive initial data is nonoscillatory. Upper and lower bounds are given for the distance between successive zeros in terms of $T_1 $ and the delay a.