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Russian Journal of Nonlinear Dynamics, 2023, Volume 19, Number 3, Pages 383–388
DOI: https://doi.org/10.20537/nd230906 (Mi nd860) 		 
Mathematical problems of nonlinearity

A Note on Forced Oscillations in Systems on a Plane

I. Yu. Polekhinabcd

a Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, 141701 Russia
b Demidov Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000 Russia
c Steklov Mathematical Institute of the Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
d Lomonosov Moscow State University, Leninskie Gory, Moscow, 119234 Russia
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DOI: https://doi.org/10.20537/nd230906
Abstract: A sufficient condition for the existence of forced oscillations in nonautonomous systems on a plane is presented under the assumption that the magnitude of the nonautonomous perturba- tion is small. An advantage of the results presented over analytic methods is that they can be applied in degenerate systems as well.
Keywords: periodic systems, forced oscillations, systems on a plane, degenerate systems, center.
Funding agency Grant number
Russian Science Foundation 19-71-30012
This work was supported by the Russian Science Foundation (Agreement No. 19-71-30012).
Received: 17.03.2023
Accepted: 28.06.2023
Bibliographic databases:
Document Type: Article
MSC: 70K40, 34C15
Language: English
Citation: I. Yu. Polekhin, “A Note on Forced Oscillations in Systems on a Plane”, Rus. J. Nonlin. Dyn., 19:3 (2023), 383–388
Citation in format AMSBIB
\Bibitem{Pol23}
\by I. Yu. Polekhin
\paper A Note on Forced Oscillations in Systems on a Plane
\jour Rus. J. Nonlin. Dyn.
\yr 2023
\vol 19
\issue 3
\pages 383--388
\mathnet{http://mi.mathnet.ru/nd860}
\crossref{https://doi.org/10.20537/nd230906}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4665100}
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