# Turkish Journal of Mathematics

## DOI

10.55730/1300-0098.3354

## Abstract

The purpose of this paper is to study the distribution of zeros of solutions to a first-order neutral differential equation of the form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' + q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for the distance between consecutive zeros of solutions, which improve upon many of the previously known ones. The results are formulated so that they can be generalized without much effort to equations for which the distribution of zeros problem is related to the study of this property for a first-order delay differential inequality. The strength of our results is demonstrated viatwo illustrative examples.

## Keywords

Distribution of zeros, neutral differential equations, oscillation

## First Page

195

## Last Page

212

## Recommended Citation

ATTIA, EMAD R.; AL-MASARER, OHOUD N.; and JADLOVSKA, IRENA
(2023)
"On the distribution of adjacent zeros of solutions to first-order neutral differential equations,"
*Turkish Journal of Mathematics*: Vol. 47:
No.
1, Article 13.
https://doi.org/10.55730/1300-0098.3354

Available at:
https://journals.tubitak.gov.tr/math/vol47/iss1/13