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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 4, Pages 226–233 (Mi timm439)  
This article is cited in 8 scientific papers (total in 8 papers)

Functional-differential equations in the space of functions of bounded variation

A. N. Sesekin, Yu. V. Fetisova

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (163 kB) Citations (8)
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Abstract: For nonlinear systems of functional-differential equations with a generalized action on the right-hand side, the notion of a solution is formalized based on the closure of smooth solutions in the space of functions of bounded variation. Sufficient conditions are obtained for the existence and uniqueness of the solution. For linear systems with distributed delay and generalized action in the system matrix, conditions for the existence of a solution and the Cauchy formula for representing the solution are derived.
Keywords: generalized action, discontinuous solution, functional-differential equation, delay.
Received: 26.05.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 269, Issue 1, Pages S258–S265
DOI: https://doi.org/10.1134/S0081543810060210
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. N. Sesekin, Yu. V. Fetisova, “Functional-differential equations in the space of functions of bounded variation”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 226–233; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S258–S265
Citation in format AMSBIB
\Bibitem{SesFet09}
\by A.~N.~Sesekin, Yu.~V.~Fetisova
\paper Functional-differential equations in the space of functions of bounded variation
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 226--233
\mathnet{http://mi.mathnet.ru/timm439}
\elib{https://elibrary.ru/item.asp?id=12952768}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S258--S265
\crossref{https://doi.org/10.1134/S0081543810060210}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866766506}
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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