Interval oscillation criteria for nonlinear second-order differential equations

New oscillation criteria are established for the nonlinear differential equation (r(t) y ' (t))' + q(t)f(y(t)) = 0 that are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t(0), infinity), rather than on the whole half-line. Our results are sharper than some. previous results. In particular, several examples that dwell upon the sharp conditions of our results are also included.