Oscillatory Behavior of Linear Neutral Delay Dynamic Equations on Time Scales

By employing the Riccati transformation technique some new oscillation criteria for the second-order neutral delay dynamic equation (y(t) + r(t) y(tau(t)))(Delta Delta) + p(t) y(delta(t)) = 0, on a time scale T are established. Our results as a special case when T = R and T = N improve some well known oscillation criteria for second order neutral delay differential and difference equations, and when T = q(N), i.e., for second-order q-neutral difference equations our results are essentially new and can be applied on different types of time scales. Some examples are considered to illustrate the main results.