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Asymptotic behavior of solutions of perturbed linear systems


Author: L. E. Bobisud
Journal: Proc. Amer. Math. Soc. 35 (1972), 457-463
MSC: Primary 34D05
DOI: https://doi.org/10.1090/S0002-9939-1972-0301313-7
MathSciNet review: 0301313
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Abstract: The existence of solutions of the system $ y' + Ay = f(t,y)$ having the form $ y(t) = Z(t)a(t)$ is proved, where $ Z(t)$ satisfies $ Z' + AZ = 0$ and the vector $ a(t)$ has limit $ \alpha $ as t increases. Estimates for the rate of convergence to zero of $ a(t) - \alpha $ and of $ y(t) - Z(t)\alpha $ are obtained.

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DOI: https://doi.org/10.1090/S0002-9939-1972-0301313-7
Keywords: Asymptotic behavior, perturbations
Article copyright: © Copyright 1972 American Mathematical Society

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