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 ) + 1 τ e x t − τ + f ( t , x t − τ 1 , … , x t − τ s ) = 0 , t ≥ 0 , where τ , τ 1 , τ 2 , … , τ s 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.