Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Dynamic behavior from asymptotic expansions

Authors: Jack K. Hale and Luiz Carlos Pavlu
Journal: Quart. Appl. Math. 41 (1983), 161-168
MSC: Primary 34C25; Secondary 34C27
DOI: https://doi.org/10.1090/qam/700669
MathSciNet review: 700669
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Abstract: The purpose of this paper is to discuss stability properties of solutions of periodic and almost-periodic differential equations containing a small parameter. The existence of the solution can be obtained in the first approximation but the stability only after $ k$ approximations. We obtain the results using asymptotic expansions, higher-order averaging and the concept of exponential hyperbolicity of order $ k$.

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DOI: https://doi.org/10.1090/qam/700669
Article copyright: © Copyright 1983 American Mathematical Society

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