OSCILLATION OF SECOND-ORDER NONLINEAR IMPULSIVE DYNAMIC EQUATIONS WITH A DAMPING TERM ON TIME SCALES

In this paper, we use Riccati transformation technique and the impulsive inequality to establish some new oscillation criteria for the second-order nonlinear impulsive dynamic equation with a damping term (r(t)(x(Delta)(t))(alpha))(Delta) + q(t)(x(Delta)(t))(alpha) + f(t, x(sigma(t))) = 0, t >= t(0), t not equal t(k), x(t(k)(+)) = g(k) (x (t(k)(-))), x(Delta)(t(k)(+)) = h(k) (x(Delta)(t(k)(-))), k = 1, 2, ..., x(t(0)(+)) = x(0), x(Delta)(t(0)(+)) = x(0)(Delta), on a time scale T. Our results generalize and extend some previous results and can be applied to some oscillation problems not discussed before. Finally, we give some examples to illustrate our main results.