Oscillation Results of Higher Order Nonlinear Neutral Delay Differential Equations with Oscillating Coefficients

In this paper, we shall consider higher order nonlinear neutral delay differential equation of the type [x(t) + p(t)x(τ(t))] + q(t) [x(σ(t))] = 0, t ≥ t0, n ∈ N, (*) where p ∈ C ([t0,∞) ,R) is oscillatory and lim t→∞ p(t) = 0, q ∈ C ( [t0,∞) ,R ) , τ, σ ∈ C ([t0,∞) ,R), τ(t), σ(t) < t, lim t→∞ τ(t) = lim t→∞ σ(t) =∞ and α ∈ (0,∞) is a ratio of odd positive integers. If α ∈ (0, 1), equation (*) is called a sublinear equation, when α ∈ (1,∞), it is called a superlinear equation. We obtain sufficient conditions for the oscillation of all solutions of this equation. AMS Subject Classifications: 39A10.