Oscillations of second-order nonlinear impulsive ordinary differential equations

Consider the second-order impulsive ordinary differential equation (r(t)(x'(t))(sigma))' + f(t,x(t)) = 0, t greater than or equal to t(o), t not equal t(k), k = 1, 2.., x(t(k)(+)) = g(k)(x(t(k))), x'(t(k)(+)) = h(k) (x'(t(k))), k = 1, 2,. (E) where 0 less than or equal to t(o) <...< t(k) <... with lim(k-->infinity) t(k) = +infinity, sigma is any quotient of positive odd integers. We obtain some sufficient conditions ensuring that all solutions of (E) oscillate. (C) 2003 Elsevier B.V. All rights reserved.