A note on Kamenev type theorems for second order matrix differential systems

Abstract:

Some oscillation criteria are given for the second order matrix differential system $Y''+Q(t) Y=0$, where $Y$ and $Q$ are $n\times n$ real continuous matrix functions with $Q(t)$ symmetric, $t\in [t_0,\infty )$. These results improve oscillation criteria recently discovered by Erbe, Kong and Ruan by using a generalized Riccati transformation $V(t)=a(t)\{Y’(t) Y^{-1}(t) +f(t)I\}$, where $I$ is the $n\times n$ identity matrix, $f\in C^1$ is a given function on $[t_0,\infty )$ and $a(t)=\exp \{-2 \int ^t f(s) ds\}$.