Oscillation Test for Linear Delay Differential Equation with Nonmonotone Argument

Abstract

In this article, we analyze the first order linear delay differential equation x 0 (t) + p(t)x (τ(t)) = 0, t ≥ t0, where p, τ ∈ C ([t0, ∞),R + ) and τ(t) ≤ t, limt→∞ τ(t) = ∞. Under the assumption that τ(t) is not necessarily monotone, we obtain new sufficient criterion for the oscillatory solutions of this equation. We also give an example illustrating the result.