Oscillation criteria for second order quasilinear neutral delay differential equations on time scales

In this paper, we consider the second-order quasilinear neutral dynamic equation (r(t)vertical bar Z(Delta)(t)vertical bar(alpha-1)Z(Delta)(t))(Delta) + q(t)vertical bar x(delta(t))vertical bar(beta-1) x(delta(t)) = 0, on a time scale T, where Z(t) = x(t) p(t)x(tau(t)), alpha, beta > alpha are constants, and obtain oscillation criteria for the equation when beta > alpha, beta = alpha and beta < alpha, respectively. Our results extend some known results when p(t) = 0 in the literature and contain the continuous and discrete cases as special cases. (C) 2011 Elsevier Ltd. All rights reserved.