Oscillation of Certain Nonlinear Second-order Damped Delay Dynamic Equations on Time Scales

The paper present some oscillation criteria for the nonlinear second-order damped delay dynamic equation ( r(t)|x∆(t)|β−1x∆(t) )∆ + p(t)|x∆σ (t)|β−1x∆σ (t) + q(t)f(x(τ(t))) = 0 on an arbitrary time scale T, where β > 0 is a constant, supT = ∞, σ(t) := inf{s ∈ T : s > t} is the forward jump operator on T, and x∆σ := x ◦ σ. Our results improve and extend some known results in which β > 0 is a quotient of odd positive integers. Examples are given to illustrate our main results.