Interval oscillation criteria for second order self-adjoint matrix differential systems with damping
Tom 79 / 2002
Annales Polonici Mathematici 79 (2002), 185-198 MSC: 34A30, 34C10. DOI: 10.4064/ap79-2-8
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.