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 equationx(t)+p(t)x(t-τ)′+Q(t)x(t-σ)=0,t⩾t0,wherep∈C[t0,∞),[0,∞),Q∈C[t0,∞),(0,∞)andτ,σ∈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.