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


Authors: Zong Qi Deng and Shi Gui Ruan
Journal: Proc. Amer. Math. Soc. 113 (1991), 777-783
MSC: Primary 34C10
DOI: https://doi.org/10.1090/S0002-9939-1991-1070514-7
MathSciNet review: 1070514
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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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DOI: https://doi.org/10.1090/S0002-9939-1991-1070514-7
Keywords: Oscillation with respect to partial variable, prepared solutions, secondorder differential systems
Article copyright: © Copyright 1991 American Mathematical Society

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