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Abstract

By using the generalized Riccati technique and the averaging technique, we establish new oscillation criteria for the second order self-adjoint matrix differential system with damping $$ (P(t)Y'(t))'+r(t)P(t)Y'(t)+Q(t)Y(t)=0,\qquad t \geq t_0. $$ The criteria are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of $[t_0,\infty ),$ rather than on the whole half-line. In particular, our results complement a number of existing results and handle a case that is not covered by known criteria. Moreover, examples indicating the importance of our results are also included.