Interval oscillation criteria for second-order nonlinear differential equations with damping

New oscillation criteria are established for the nonlinear damped differential equation (ry′)′ +py′ + qf(y) = 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 [t0, ∞), rather than on the whole half-line. Our results are sharper than some previous results, and extend and improve the recent interval criteria of Kong and Huang, and can be applied to extreme cases such as ∫∞t0 q(s) DS = −∞. In particular, several examples that dwell upon the sharp conditions of our results are also included.