Improved oscillation criteria for first-order delay differential equations with variable delay

Abstract

This article concerns the oscillation of solutions to the delay differential equation x′(t) + p(t)x(τ(t)) = 0. Conditions for oscillation have been stated as lower bounds for the limit superior and limit inferior of ∫tτp. 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.