Consider the first-order linear delay differential equation x′(t) + p(t)x(τ(t)) = 0, t ≥ t_0, (1) where p, τ ∈ C([t_0,∞),R~+), τ(t) < t for t ≥ t_0 and lim_(t→∞)τ(t) = ∞, and the (discrete analogue) difference equation ?x(n) + p(n)x(τ(n)) = 0, n = 0, 1, 2,..., (1′) where ? denotes the forward difference operator ?x(n) = x(n + 1) - x(n), p(n) is a sequence of nonnegative real numbers and τ(n) is a sequence of integers such that τ(n) ≤ n-1 for all n ≥ 0 and lim_(n→∞)τ(n) = 1. The state-of-the-art on the oscillation of all solutions to these equations are established especially in the case of non-monotone arguments. Examples illustrating the results are given.
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