New nonoscillation criteria for delay differential equations ✩

This paper is concerned with the nonoscillation of first order delay differential equations of the form x (t )+ p(t)x τ(t) = 0, t t0, where p, τ ∈ C([t0,∞),R+), R+ = [0,∞), τ(t) is nondecreasing, τ(t) < t for t t0 and limt→∞τ(t)=∞. New nonoscillation conditions are obtained. These conditions concern the case when the well-known nonoscillation condition t τ(t) p(s) ds 1/e is not satisfied.  2003 Published by Elsevier Inc