Linearized Oscillation Of Even Order Nonlinear Neutral Delay Differential Equations∗

In this paper, we proved the even order nonlinear neutral delay differential equation [x(t) − p(t)g(x(t − τ))](n) = q(t)h(x(t − σ)) has the same oscillatory character as its linearized equation [x(t) − p0x(t − τ)](n) = q0x(t − σ) under some rather relaxed conditions on g(u) and h(u), where p0 = limt→ ∞ p(t), q0 = limt→ ∞ q(t).