Oscillation and asymptotic behaviour of a higher-order nonlinear neutral-type functional differential equation with oscillating coefficients

We will study oscillation of bounded solutions of higher-order nonlinear neutral delay differential equations of the following type: [y(t)+p(t)f(y((t)))] (n) + q (t) h (y (δ(t))) = 0,t ≥ t 0,t ∈ r,where p ∈ c ([t0,ℝ),r),limt → ∞ p (t) = 0,q ∈ c ([t0,∞ ),ℝ+),τ(t),δ(t) ∈ c ([ t0,∞ ),ℝ),τ(t),δ(t) < t,lim t → ∞ τ(t),δ(t) = ∞,and f,h ∈ c (ℝ,ℝ). we obtain sufficient conditions for the oscillation of all solutions of this equation. © 2011 mustafa kemal yildiz et al.