New oscillation criteria for linear delay differential equations

We obtain new sufficient conditions for the oscillation of all solutions of the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, with p(t) ≥ 0, τ(t) < t. Our results improve the known results in the literature which include those obtained recently in papers by Elbert and Stavroulakis, Li, and Yu et al.