The distribution of zeros of all solutions of first order neutral differential equations

This paper is concerned with the distribution of zeros of all solutions of the first-order neutral differential equation x ( t ) + p ( t ) x ( t - ? ) ' + Q ( t ) x ( t - ? ) = 0 , t ? t 0 , where p ? C t 0 , ∞ ) , 0 , ∞ ) , Q ? C t 0 , ∞ ) , ( 0 , ∞ ) and ? , ? ? R + . New estimations for the distance between adjacent zeros of this neutral equation are obtained via comparison with a corresponding differential inequality. These results extend some known results from the non-neutral to the neutral case and improve other published results as well.