Oscillation Criteria for Nonlinear Delay Differential Equations of Second Order

We prove oscillation theorems for the nonlinear delay differential equation (vertical bar y'(t)(alpha-2) y'(t)' + q(t) vertical bar y(tau(t))vertical bar(beta-2) y(tau(t)) = 0, t >= t(*) > 0, where beta > 1, alpha > 1, q(t) >= 0 and locally integrable on [t(*), infinity), tau(t) is a continuous function satisfiying 0 < tau(t) <= t and lim(t ->infinity) tau(t) = infinity. The results obtained essentially improve the known results in the literature and can be applied to linear and half-linear delay type differential equations.