Abstract
We use the generalized Riccati transformation and the inequality technique to establish some new oscillation criteria for the second-order nonlinear delay dynamic equation with damping on a time scaleT(r(t)g(x(t),xΔ(t)))Δ+p(t)g(x(t),xΔ(t)) + q(t)f(x(τ(t)))=0,wherer(t),p(t), andq(t)are positive right dense continuous (rd-continuous) functions onT. Our results improve and extend some results established by Zhang et al., 2011. Also, our results unify the oscillation of the second-order nonlinear delay differential equation with damping and the second-order nonlinear delay difference equation with damping. Finally, we give some examples to illustrate our main results.
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