Oscillation and Asymptotic Behavior for nth-order Nonlinear Neutral Delay Dynamic Equations on Time Scales

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)psi(x(t)) [vertical bar(x(t) +p(t)x(tau(t)))(Delta n-1)vertical bar(alpha-1)(x(t) + p(t)x(tau(t)))(Delta n-1)](gamma)](Delta) + lambda F(t, x(delta(t))) = 0, on time scales, where alpha > 0 is a constant, gamma > 0 is a quotient of odd positive integers and lambda = +/-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.