Oscillations of delay differential equations with variable coefficients

Abstract

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 = ∞. © 1995 Academic Press. All rights reserved.