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 $\dot y = A(t)y$.
- J. W. Bebernes and N. X. Vinh, On the asymptotic behavior of linear differential equations, Amer. Math. Monthly 72 (1965), 285ā€“287. MR 181784, DOI https://doi.org/10.2307/2313699
- I. Norman Katz, Asymptotic behavior of solutions to some $n$th order linear differential equations, Proc. Amer. Math. Soc. 21 (1969), 657ā€“662. MR 239199, DOI https://doi.org/10.1090/S0002-9939-1969-0239199-1
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Additional Information
Keywords:
Asymptotic behavior,
linear system,
fundamental matrix,
variation of parameter,
Gronwall inequality,
Liouvilleā€™s theorem,
Wronskian
Article copyright:
© Copyright 1970
American Mathematical Society