Oscillation and asymptotic behavior for nth-order nonlinear neutral delay dynamic equations on time scales

摘要

In this paper, we derive some sufficient conditions for the oscillation and asymptotic behavior of the nth-order nonlinear neutral delay dynamic equations {a(t)Ψ(x(t))[|(x(t)+p(t)x(τ(t)))~(Δn-1|α-1) (x(t)+p(t)x(au(t)))~(Δn-1)]~γ} ~Δ + λ F(t,xδ(t))) = 0, on time scales, where α > 0 is a constant, γ>0 is a quotient of odd positive integers and λ = ±1. Our results in this paper not only extend and improve some known results but also present a valuable unified approach for the investigation of oscillation and asymptotic behavior of nth-order nonlinear neutral delay differential equations and nth-order nonlinear neutral delay difference equations. Examples are provided to show the importance of our main results.