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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the asymptotic behavior of linear systems


Author: Phil Locke
Journal: Proc. Amer. Math. Soc. 25 (1970), 93-95
MSC: Primary 34.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0252767-4
MathSciNet review: 0252767
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Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to establish a necessary and sufficient condition for the vector-matrix system $\dot x = [A(t) + B(t)]x$ to have solutions of the form $Y(t)c(t)$ where $Y(t)$ is a fundamental matrix of solutions of $\dot y = A(t)y$.


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Keywords: Asymptotic behavior, linear system, fundamental matrix, variation of parameter, Gronwall inequality, Liouvilleā€™s theorem, Wronskian
Article copyright: © Copyright 1970 American Mathematical Society