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Proceedings of the American Mathematical Society

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

 

 

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: 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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DOI: https://doi.org/10.1090/S0002-9939-1970-0252767-4
Keywords: Asymptotic behavior, linear system, fundamental matrix, variation of parameter, Gronwall inequality, Liouville's theorem, Wronskian
Article copyright: © Copyright 1970 American Mathematical Society