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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2011, Number 12, Pages 30–41 (Mi ivm8403)  
This article is cited in 4 scientific papers (total in 4 papers)

Stability of a linear difference equation and estimation of its fundamental solution

A. Yu. Kulikov, V. V. Malygina

Chair of Computational Mathematics and Mechanics, Perm State Technical University, Perm, Russia
Full-text PDF (229 kB) Citations (4)
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Abstract: We consider a linear nonautonomous system of difference equations. Under natural restrictions we prove that the stability with respect to the initial function and that with respect to the right-hand side in spaces of bounded and summable functions are equivalent to the corresponding estimates for the fundamential solution. As a consequence, we obtain an effective stability condition for a system with a constant matrix.
Keywords: difference equations, stability, fundamental solution, effective conditions.
Received: 09.11.2010
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, Volume 55, Issue 12, Pages 23–33
DOI: https://doi.org/10.3103/S1066369X11120048
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: A. Yu. Kulikov, V. V. Malygina, “Stability of a linear difference equation and estimation of its fundamental solution”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 12, 30–41; Russian Math. (Iz. VUZ), 55:12 (2011), 23–33
Citation in format AMSBIB
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\by A.~Yu.~Kulikov, V.~V.~Malygina
\paper Stability of a~linear difference equation and estimation of its fundamental solution
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 12
\pages 30--41
\mathnet{http://mi.mathnet.ru/ivm8403}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2963461}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 12
\pages 23--33
\crossref{https://doi.org/10.3103/S1066369X11120048}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84856237424}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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