Oscillation Theorems of the Second Order Linear Matrix Differential System with Damping

By using the Riccati technique and the technique, new oscillation criteria are obtained for the second order matrix differential system(P(t)Y′(t))′ r(t)P(t)Y′(t) Q(t)Y(t) = 0, t≥t0.These results in the present paper generalize and improve many known conclusions. Furthermore, some results are different from the 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. In particular, our results complement a number of existing results and handle the ease that is not covered by the known criteria.

Oscillation Theorems of the Second Order Linear Matrix Differential System with Damping

By using the Riccati technique and the technique, new oscillation criteria are obtained for the second order matrix differential system (P(t)Y'(t))' + r(t)P(t)Y'(t) + Q(t)Y (t) = 0, t ≥ t ₀. These results in the present paper generalize and improve many known conclusions. Furthermore, some results are different from the most known ones in the sense that they are based on the information only on a sequence of subintervals of t ₀,∞), rather than on the whole half–line. In particular, our results complement a number of existing results and handle the case that is not covered by the known criteria. This work is supported by National Key Basic Research Special Fundation of China (No. G1998020309), National Natural Science Foundation of China (No. 10461002) and Science Foundation of Guangxi Province of China (No. 0236012)