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Kamenev type theorems for second-order matrix differential systems

Authors: Lynn H. Erbe, Qingkai Kong and Shi Gui Ruan
Journal: Proc. Amer. Math. Soc. 117 (1993), 957-962
MSC: Primary 34C10; Secondary 34A30
MathSciNet review: 1154244
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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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Keywords: Matrix differential system, oscillation theory, Riccati equation
Article copyright: © Copyright 1993 American Mathematical Society

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