Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Sbornik: Mathematics, 2014, Volume 205, Issue 6, Pages 862–891
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004401 (Mi sm8233) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action

A. I. Dvirnyja, V. I. Slyn'kob

a Hedmark University College
b Institute of Mechanics named after S. P. Timoshenko of National Academy of Sciences of Ukraine
English version PDF (609 kB) Citations (7) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/SM2014v205n06ABEH004401
Abstract: Inverse theorems to Lyapunov's direct method are established for quasihomogeneous systems of differential equations with impulsive action. Conditions for the existence of Lyapunov functions satisfying typical bounds for quasihomogeneous functions are obtained. Using these results, we establish conditions for an equilibrium of a nonlinear system with impulsive action to be stable, using the properties of a quasihomogeneous approximation to the system. The results are illustrated by an example of a large-scale system with homogeneous subsystems.
Bibliography: 30 titles.
Keywords: impulsive action, quasihomogeneous system, Lyapunov stability, Lyapunov's direct method.
Received: 24.03.2013 and 09.12.2013
Bibliographic databases:
Document Type: Article
UDC: 517.925.51
MSC: Primary 35R12; Secondary 34A37
Language: English
Original paper language: Russian
Citation: A. I. Dvirnyj, V. I. Slyn'ko, “Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action”, Sb. Math., 205:6 (2014), 862–891
Citation in format AMSBIB
\Bibitem{DviSly14}
\by A.~I.~Dvirnyj, V.~I.~Slyn'ko
\paper Investigating stability using nonlinear quasihomogeneous approximation to differential equations with impulsive action
\jour Sb. Math.
\yr 2014
\vol 205
\issue 6
\pages 862--891
\mathnet{http://mi.mathnet.ru//eng/sm8233}
\crossref{https://doi.org/10.1070/SM2014v205n06ABEH004401}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3241830}
\zmath{https://zbmath.org/?q=an:06349854}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014SbMat.205..862D}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000344080300005}
\elib{https://elibrary.ru/item.asp?id=21826630}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84907340549}
Linking options:
  • https://www.mathnet.ru/eng/sm8233
  • https://doi.org/10.1070/SM2014v205n06ABEH004401
  • https://www.mathnet.ru/eng/sm/v205/i6/p109
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024