Kamenev type theorems for second-order matrix differential systems

Erbe, Lynn H.; Kong, Qingkai; Ruan, Shi Gui

doi:10.1090/S0002-9939-1993-1154244-0

Kamenev type theorems for second-order matrix differential systems
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by Lynn H. Erbe, Qingkai Kong and Shi Gui Ruan

Proc. Amer. Math. Soc. 117 (1993), 957-962

DOI: https://doi.org/10.1090/S0002-9939-1993-1154244-0

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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.

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