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)\(alpha-1) x x'(t)]' + q(t)\x(t)\(alpha-1) x(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 [t(0), infinity), 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 integral(t0)(infinity) q(s)ds = -infinity. In particular, several interesting examples that 0 illustrate the importance of our results are included. (C) 2003 Elsevier Inc. All rights reserved.