An improved oscillation criteria for first order dynamic equations

Abstract

In this work, we consider the first-order dynamic equations x ∆(t) + p(t)x (τ (t)) = 0, t ∈ [t0, ∞)T where p ∈ Crd ( [t0, ∞)T, R + ) , τ ∈ Crd ([t0, ∞)T, T) and τ (t) ≤ t, limt→∞ τ (t) = ∞. When the delay term τ (t) is not necessarily monotone, we present a new sufficient condition for the oscillation of first-order delay dynamic equations on time scales.