Oscillations of Delay Differential Equations with Variable Coefficients

Consider the delay differential equation ẋ(t) + p(t)x(t − τ) = 0, where p(t) ∈ C[[t0, ∞), R+] and τ is a positive constant. We show that every solution of this equation oscillates if ∫tt−τp(t) dt ≥ 1/e for sufficiently large t and ∫∞t0+τp(t)[exp(∫tt−τp(s) ds − 1/e) − 1] dt = ∞.