Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales

By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation - mathematical expression is present -, on a time scale double-sturck T sign . The results improve some oscillation results for neutral delay dynamic equations and in the special case when double-sturck T sign = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established by Li and Liu [Canad. J. Math., 48 (1996), 871-886]. When double-sturck T sign = ℕ , our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh [Comp. Math. Appl., 36 (1998), 123-132]. When - mathematical expression is present - our results are essentially new. Some examples illustrating our main results are given.