Oscillation criteria of second-order nonlinear delay dynamic equations on time scales

By means of Riccati transformation technique, we will establish some new oscillation criteria for the second-order nonlinear delay dynamic equation (p(t) (x^Δ(t)^y)^Δ +q(t)f(x(t(t))) = 0 on a time scale T; here γ ≥ 1 is an odd positive integers with p and q real-valued positive functions defined on T. Our results improve and extend some results established by Saker [S. H. Saker, Oscillation criteria of second-order half-linear dynamic equations on time scales, J. Comp. Appl. Math. 177 (2005) 375-387; S. H. Saker, Oscillation of nonlinear dynamic equations on time scales, Appl. Math. Comput. 148 (2004) 81-91] and Sahiner [Y. Sahiner, Oscillation of second-order delay differential equations on time scales, Nonlinear Analysis, TMA, 63 (2005) 1073-1080] but also unify the oscillation of the second order nonlinear delay differential equation and the second order nonlinear delay difference equation.