Interval criteria for oscillation of second-order half-linear differential equations ✩

By employing a generalized Riccati technique and an integral averaging method, interval oscillation criteria are established for the second-order half-linear differential equation [r(t)|x (t )|α−1 × x (t )] + q(t)|x(t)|α−1x(t) = 0. These criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [t0,∞), rather than on the whole half-line. They also extend, improve, and complement a number of existing results, and can be applied to extreme cases such as ∞t0 q(s)ds = −∞. In particular, several interesting examples that illustrate the importance of our results are included.  2003 Elsevier Inc. All rights reserved.