Interval criteria for oscillation of certain matrix differential systems ✩

By employing a generalized Riccati technique and an averaging technique, interval oscillation criteria are established for the second order matrix differential system of the form [P(t)Y ] +Q(t )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 presented in the form of a high degree of generality, handle the cases which are not covered by known criteria and can be applied to extreme cases such as limt→∞λ1[ t t0 Q(s) ds] =−∞. In particular, several interesting examples that dwell upon the importance of our results are included.  2002 Elsevier Science (USA). All rights reserved.