Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 32, pp. 1-12.

Title: Improved oscillation criteria for first-order delay differential equations
       with variable delay
       
Author: Julio G. Dix (Texas State Univ., San Marcos, Texas, USA)

Abstract:
 This article concerns the oscillation of solutions to the delay differential equation
 $x'(t)+p(t)x(\tau(t))=0$.
 Conditions for oscillation have been stated as lower bounds for the limit superior and
 limit inferior of $\int_\tau^t p$.
 In this article we match the bound for the best case in [7],
 without using one of their hypotheses.
 Then assuming that hypothesis, we obtain a bound lower than the one in [12].
 Then we apply our results to an equation with several delays.
 We employ iterated estimates of the solution.

Submitted January 29, 2021. Published April 24, 2021.
Math Subject Classifications: 34K11, 34C10.
Key Words: Oscillation of solutions; first-order delay differential equation;
           eventually positive solution.