Interval oscillation criteria for second order self-adjoint matrix differential systems with damping

Qigui Yang¹

¹ Department of Mathematics Guangxi Normal University Guilin, 541004, P.R. China and Department of Mathematics Zhongshan University Guangzhou, 510275, P.R. China

Annales Polonici Mathematici, Tome 79 (2002) no. 2, pp. 185-198.

Résumé

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.

Détail

DOI : 10.4064/ap79-2-8

Keywords: using generalized riccati technique averaging technique establish oscillation criteria second order self adjoint matrix differential system damping t t t qquad geq criteria different known sense based information only sequence subintervals infty rather whole half line particular results complement number existing results handle covered known criteria moreover examples indicating importance results included