A oscillation theorem for a class of even order neutral differential equations

The even order neutral differential equation dⁿ/dtⁿ[x(t) + h(t)x(t - τ)] + f(t,x(g(t)))=0 is considered under the following conditions: n ≥ 2 is even; τ > 0; h ∈ C(R); g ∈ C [t₀,∞), lim_t→∞ g(t) = ∞; f ∈ C([t₀, ∞) × R), uf(t, u) ≥ 0 for (t, u) ∈ [t₀, ∞) × R, and f (t, u) is nondecreasing in u ∈ R for each fixed t ≥ t₀. It is shown that (1) is oscillatory if and only if the certain non-neutral differential equation is oscillatory, for the case where 0 ≤ μ ≤ h(t) ≤ λ < 1 or 1 < λ ≤ h (t) ≤ μ.