Oscillation of second-order nonlinear delay dynamic equations on time scales

In this work, we use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation p t xΔ t γ Δ q t f x τ t 0, on a time scale T, where γ is the quotient of odd positive integers and p(t) and q(t) are positive right-dense continuous rd-continuous functions on T. Our results improve and extend some results established by Sun et al. 2009. Also our results unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation. Finally, we give some examples to illustrate our main results.