二阶线性矩阵微分系统的振动性

On the Oscillation of Second Order Linear Matrix Differential Systems

本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0，t∈［t0，∞）．其中P，Q和Y是n×n实连续矩阵函数，且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0，t∈［t0，∞））．利用推广的Riccati变换，得到了系统（1）振动的若干新判据．所得结果改进了Erbe，Kong和Ruan的相应结果．

In the present paper matrix differential system of the form (P(t)Y')' + Q(t)Y = 0, t ∈ [t0, ∞) is considered, where P,Q and Y are n x n real continuous matrix functions, p(t) and Q(t) are symmetric, and p(t) > 0, t ∈ [t0,∞). Using Riccati transformation generalized some new oscillation criteria for the system are established. The criteria obtained improve Erbe, Kong and Ruan's results in [4].