Kamenev type theorems for second-order matrix differential systems

Abstract:

We consider the second order matrix differential systems (1) $(P(t)Y’)’ + Q(t)Y = 0$ and (2) $Y'' + Q(t)Y = 0$ where $Y,\;P$ and $Q$ are $n \times n$ real continuous matrix functions with $P(t),\;Q(t)$ symmetric and $P(t)$ positive definite for $t \in [{t_0},\infty )\;(P(t) > 0,t \geqslant {t_0})$. We establish sufficient conditions in order that all prepared solutions $Y(t)$ of (1) and (2) are oscillatory. The results obtained can be regarded as generalizing well-known results of Kamenev in the scalar case.