On the distribution of zeros of solutions of a first order neutral differential equation

Document Type : Original articles

Authors

Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt

Abstract

This paper is devoted to study the distribution of zeros of all solutions of the first-order neutral
differential equation
[x(t) — px(t — T)]' + Q(t)x(t — σ) = 0, t > t0,
where p > 1, τ,σ > 0 , and Q ∈ C([t0, ∞), (0, ∞)).
We obtain new estimates for the distance between adjacent zeros of all solutions of the above equation
under suitable criteria. Our results are supported with illustrative examples.

Keywords