Oscillation Tests for Delay Equations

Abstract

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form (1) x′(t) + p(t)x(τ(t)) = 0, t ≥ T, where p, τ ∈ C([T,∞),R+), R+ = [0,∞), τ(t) is nondecreasing, τ(t) < t for t ≥ T and limt→∞ τ(t) = ∞. Let the numbers k and L be defined by