Interval criteria for oscillation of second-order nonlinear neutral differential equations

Some new oscillation criteria are established in this paper for the second-order nonlinear neutral delay differential equation [r(t)(x(t) + p(t)x(t−τ))′]′ + q(t)f(x(t−)δ)) = 0, where τ and δ are nonnegative constants, r, p, q ε C([t0, ∞), R), and f ε C(R, R). These results 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 about neutral and delay differential equations. In particular, several examples that dwell upon the sharp conditions of our results are also included.