A necessary and sufficient condition for the oscillation in a class of even order neutral differential equations

The even order neutral differential equation (1.1) (equation presented) is considered under the following conditions: n ≥ 2 is even; λ > 0; T > 0; 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 equation (1.1) is oscillatory if and only if the non-neutral differential equation (equation presented) is oscillatory.