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

This article is cited in 2 scientific papers (total in 2 papers)

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 МК-139.2017.1


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

Full text: PDF file (455 kB)
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English version:
Mathematical Notes, 2018, 104:2, 253–262

Bibliographic databases:

UDC: 517.925.54
Received: 18.05.2017

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
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  • 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  mathnet  crossref  crossref  isi  elib
    2. K. S. Lapin, “Totalnaya ogranichennost po Puassonu reshenii $\mathcal{P}$-vozmuschennykh slozhnykh sistem differentsialnykh uravnenii”, Izv. vuzov. Matem., 2019, no. 10, 62–74  mathnet  crossref
  • Математические заметки Mathematical Notes
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