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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: 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$.


References [Enhancements On Off] (What's this?)

  • [1] J. W. Bebernes and N. X. Vinh, On the asympotic behavior of linear differential equations, Amer. Math. Monthly 72 (1965), 285-287. MR 31 #6011. MR 0181784 (31:6011)
  • [2] I. N. Katz, Asymptotic behavior of solutions to some $ n$th order linear differential equations, Proc. Amer. Math. Soc. 21 (1969), 657-662. MR 0239199 (39:556)

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Additional Information

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

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