Interval oscillation criteria for certain forced second-order differential equations

By using generalized Riccati transformations and an inequality due to Hardy et al., several new interval oscillation criteria are established for the nonlinear damped differential equation r(t)k1(x, x0 )
0 + p(t)k2(x, x0 )x 0 + q(t)f(x) = e(t), t ≥ t0. The new interval oscillation criteria are different from most known ones in the sense they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. Our results improve and extend the known some results in the literature.