New oscillatory criteria for higher-order nonlinear neutral delay differential equation

In this paper, we consider the higher-order nonlinear neutral delay differential equation equation(1.1)(x(t)−p(t)x(t−τ))(n)+f(t,x(σ(t)))=0(x(t)−p(t)x(t−τ))(n)+f(t,x(σ(t)))=0 where nn is an odd number and n⩾3,τ>0n⩾3,τ>0, p,σ∈C([t0,∞),R+),σ(t)⩽t,limt→∞σ(t)=∞p,σ∈C([t0,∞),R+),σ(t)⩽t,limt→∞σ(t)=∞, f∈C([t0,∞)×R,R),f(t,u)f∈C([t0,∞)×R,R),f(t,u) is nondecreasing in uu.