Oscillation of second-order nonlinear delay dynamic equations with damping on time scales (Q5919144)

Summary: 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 \(\mathbb{T}\) \[ (r(t) g(x(t), x^\Delta(t)))^\Delta+ p(t) g(x(t), x^\Delta(t))+ q(t) f(x(r(t)))= 0, \] where \(r(t)\), \(p(t)\), and \(q(t)\) are positive right dense continuous (rd-continuous) functions on \(\mathbb{T}\). Our results improve and extend some known results. 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.