Oscillation of second order self-conjugate differential equation with impulses

In this paper, we investigate the oscillation of second-order self-conjugate differential equation with impulses (a(t)(x(t) + p(t)x(t-tau))')' + q(t)x(t - sigma) = 0, t not equal t(k), t > t(0), (1) x(t(k)(+)) = (1 + b(k))x(t(k)), k = 1, 2, (2) x'(t(k)(+))=(1+b(k))x'(t(k)), k = 1,2, (3) where a, p, q are continuous functions in [t(0), +infinity), q(t) >= 0, a(t) > 0, integral(infinity)(t0) (I/a(s)) ds = infinity, tau > 0, sigma > 0, b(k) > -1, 0 < t(0) < t(1) < t(2) < ... < t(k) < ... and lim(k ->infinity) t(k) = infinity. We get some sufficient conditions for the oscillation of solutions of Eqs. (1)-(3). (c) 2005 Elsevier B.V. All rights reserved.