Abstract:
We consider a system of ordinary first-order differential equations. The right-hand sides of the system are proportional to a small parameter and depend almost periodically on fast time and periodically on slow time. With this system, we associate the system averaged over fast time. We assume that the averaged system has a structurally unstable periodic solution. We prove a theorem on the existence and stability of almost periodic solutions of the original system.
Citation:
A. Yu. Ukhalov, “Almost-periodic solutions to systems of differential equations with fast and slow time in the degenerate case”, Mat. Zametki, 63:3 (1998), 451–456; Math. Notes, 63:3 (1998), 396–400
\Bibitem{Ukh98}
\by A.~Yu.~Ukhalov
\paper Almost-periodic solutions to systems of differential equations with fast and slow time in the degenerate case
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 451--456
\mathnet{http://mi.mathnet.ru/mzm1302}
\crossref{https://doi.org/10.4213/mzm1302}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1631901}
\zmath{https://zbmath.org/?q=an:0919.34040}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 396--400
\crossref{https://doi.org/10.1007/BF02317788}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075783100017}
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https://www.mathnet.ru/eng/mzm1302
https://doi.org/10.4213/mzm1302
https://www.mathnet.ru/eng/mzm/v63/i3/p451
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