Oscillation with respect to partial variables of linear second-order differential systems

Deng, Zong Qi; Ruan, Shi Gui

doi:10.1090/S0002-9939-1991-1070514-7

Oscillation with respect to partial variables of linear second-order differential systems
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by Zong Qi Deng and Shi Gui Ruan PDF

Proc. Amer. Math. Soc. 113 (1991), 777-783 Request permission

Abstract:

Consider the second-order vector differential system (1)$x''(t) + Q(t)x(t) = 0$ and matrix differential system (2) $X''(t) + Q(t)X(t) = 0$, where $x(t)$ is an $n$-dimensional vector function and $X(t)$ and $Q(t)$ are $n \times n$ continuous matrix functions. In this article, we establish the concept that systems (1) and (2) are oscillatory with respect to partial variables. Some sufficient conditions are obtained; several examples are given to illustrate the results.

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