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 Mat. Zametki, 2018, Volume 104, Issue 2, Pages 243–254 (Mi mz11683)

Poisson Total Boundedness of Solutions of Systems of Differential Equations and Lyapunov Vector Functions

K. S. Lapin

Mordovian State Pedagogical Institute, Saransk

Abstract: We introduce the notions of Poisson total boundedness of solutions, partial Poisson total boundedness of solutions, and partial Poisson total boundedness of solutions with partly controlled initial conditions. We use the Lyapunov vector function method to obtain sufficient conditions for the Poisson total boundedness of solutions, the partial Poisson total boundedness of solutions, and the partial Poisson total boundedness of solutions with partly controlled initial conditions. As a consequence, we obtain sufficient conditions for the above-mentioned kinds of Poisson total boundedness of solutions based on the Lyapunov function method.

Keywords: boundedness of solutions, Poisson total boundedness of solutions, Lyapunov vector function, partial boundedness of solutions, partly controlled initial conditions.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation ÌÊ-139.2017.1

DOI: https://doi.org/10.4213/mzm11683

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English version:
Mathematical Notes, 2018, 104:2, 253–262

Bibliographic databases:

UDC: 517.925.54

Citation: K. S. Lapin, “Poisson Total Boundedness of Solutions of Systems of Differential Equations and Lyapunov Vector Functions”, Mat. Zametki, 104:2 (2018), 243–254; Math. Notes, 104:2 (2018), 253–262

Citation in format AMSBIB
\Bibitem{Lap18} \by K.~S.~Lapin \paper Poisson Total Boundedness of Solutions of Systems of Differential Equations and Lyapunov Vector Functions \jour Mat. Zametki \yr 2018 \vol 104 \issue 2 \pages 243--254 \mathnet{http://mi.mathnet.ru/mz11683} \crossref{https://doi.org/10.4213/mzm11683} \elib{http://elibrary.ru/item.asp?id=35410185} \transl \jour Math. Notes \yr 2018 \vol 104 \issue 2 \pages 253--262 \crossref{https://doi.org/10.1134/S000143461807026X} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000446511500026} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85054402885} 

• http://mi.mathnet.ru/eng/mz11683
• https://doi.org/10.4213/mzm11683
• http://mi.mathnet.ru/eng/mz/v104/i2/p243

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. K. S. Lapin, “Higher-order derivatives of Lyapunov functions and ultimate boundedness in the sense of Poisson of solutions to systems of differential equations”, Siberian Math. J., 59:6 (2018), 1100–1104
2. K. S. Lapin, “Totalnaya ogranichennost po Puassonu reshenii $\mathcal{P}$-vozmuschennykh slozhnykh sistem differentsialnykh uravnenii”, Izv. vuzov. Matem., 2019, no. 10, 62–74
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