Oscillation Results of Higher Order Nonlinear Neutral Delay Differential Equations

In this paper, we shall consider higher order nonlinear neutral delay differential equation of the type[x(t)+p(t)x(τ(t))]^n+q(t)[x(σ(t))]^{∞}=0,t≥t0, n in N,where p,q in C([t0,∞),[0,∞)), τ,σ in C([t0,∞),R), τ(t) t,lim_{t→∞}τ(t)=∞, (t) t, lim_{t→∞}σ(t)=∞, and α in(0,∞) is a ratio of odd positive integers. We obtain sufficient conditions for the oscillations of all solutions of this equation.