Interval oscillation criteria for second-order nonlinear perturbed differential equations

We present new interval oscillation criteria for certain classes of second-order nonlinear perturbed differential equations which are based on the information only on a sequence of subintervals of [to, ∞), rather than on the whole half-line. Our results are sharper than those known in the literature and deal with the cases which are not covered by the known criteria. In particular, our results can be applied to extreme cases such as η∞q(s)ds = −∞. Finally, two examples which dwell upon the sharpness of the conditions of our results are also illustrated.