Oscillation criteria for nonlinear delay differential equations of second order

We prove oscillation theorems for the nonlinear delay differential equation " |y 0 (t)| −2 y 0 (t) "0 + q(t)|y((t))| −2 y((t)) = 0, tt > 0, where > 1, > 1, q(t) 0 and locally integrable on (t ,1), (t) is a continuous function satisfiying 0 < (t) t and limt!1 (t) = 1. The results obtained essentially improve the known results in the literature and can be applied to linear and half-linear delay type differential equations.