Abstract:The oscillation for certain second-order nonlinear variable delay dynamic equations with damping term and nonlinear neutral term on time scales was discussed. By using the time scales theory and the generalized Riccati transformation and the inequality technique, some new oscillation criteria for the equations were established. The results extend and improve some known results, but also unify the oscillation of second-order nonlinear delay differential equations and second-order nonlinear delay difference equations with damping term. Some examples were given to illustrate the main results of this article.

Key words:oscillation,time scales,dynamic equations,damping term,nonlinear neutral term