New oscillation criteria for first order delay differential equations in a critical state

Abstract

In this work, some new oscillation criteria are obtained for the first order delay differential equation x′ (t) + frac(1, τ e) xt - τ + f (t, xt - τ1, ..., xt - τs) = 0, t ≥ 0, where τ, τ1, τ2, ..., τs are nonnegative numbers, f is a function. Our results improve the known results from the literature, and an example of an application is given at the end. © 2006 Elsevier Ltd. All rights reserved.