New Application Of Riccati Teachique In Second Order Delay Differential Equations And Second Order Matrix Differential Systems

In this paper, we study the oscillation of the second order nonlinear delay differential equationand the second order linear matrix differential systemwhere q, f, T, g, P, Q are defined as in the sequel.As we all know, in the course of the studying about the oscillation theory of equation (A) and system (B), Riccati technique is the more important method. By applying this technique, many specialists and authors from all over the world have presented a number of oscillation results for equation (A) and system (B). For details, the reader can be referred to papers cited in this paper.But, two points should be pointed out: Firstly, most known oscillation results are limited to the assumption that the potential q(t) > 0 eventually. When we allow q(t) to change its sign, few people have studied the oscillatory behaviorof equation (A); Secondly, more existing oscillation results for equation (A) and system (B) involve the integral behavior of q or Q on some ray [to, oo). When q or Q has bad behavior on some ray [