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)vertical bar x(Delta)(t)vertical bar(beta-1)x(Delta)(t))(Delta)+p(t)vertical bar x(Delta sigma)(t)vertical bar beta-1x(Delta sigma)(t) + q(t)f(x(tau(t))) = 1 on an arbitrary time scale T, where beta > 0 is a constant, sup T = infinity, sigma(t) := inf {s epsilon T : s > t} is the forward jump operator on T, and x(Delta sigma) := x(Delta) o sigma. Our results improve and extend some known results in which beta > 0 is a quotient of odd positive integers. Examples are given to illustrate our main results.