Oscillation of Second-Order Nonlinear Delay Dynamic Equations with Damping on Time Scales

Abstract EN

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 scale T(r(t)g(x(t), xΔ(t)))Δ+p(t)g(x(t), xΔ(t)) + q(t)f(x(τ(t)))=0, where r(t), p(t), and q(t) are positive right dense continuous (rd-continuous) functions on T.

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.