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−1x′(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.