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Trudy Moskovskogo Matematicheskogo Obshchestva, 2019, Volume 80, Issue 1, Pages 113–131 (Mi mmo619)  
This article is cited in 19 scientific papers (total in 19 papers)

On the solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic

A. G. Sergeeva, Kh. A. Khachatryanb

a Steklov Mathematics Institute, Russian Academy of Science
b Institute of Mathematics NAN of Armenia
Full-text PDF (364 kB) Citations (19)
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Abstract: This paper is devoted to the investigation of solvability and asymptotic properties of solutions for some classes of nonlinear multidimensional integral equations. These equations have a direct application in the theory of the geographical spread of an epidemic. Constructive theorems of the existence of monotonous and bounded solutions are proved and qualitative properties of solutions are studied. Concrete examples of equations of the considered type, arising in real biological processes, are given.
Key words and phrases: Epidemic, nonlinear equation, iterations, monotonicity, bounded solutions.
Funding agency Grant number
Russian Foundation for Basic Research 18-51-05009_Арм_а
19-01-00474
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Science Foundation 19-11-00223
During the preparation of this article the first author was partially supported by RFFR Grants 18-51-05009 and 19-01-00747, and by the “Nonlinear Dynamics” Program of the Presudium of RAN
The second author was supported by the Russian Science Foundation Grant (project 10-11-00223)
Results presented in Sections 2 and 3 (the proof of Theorem 1) were obtained by Kh. A. Khachaturyan. Results of Sections 2 and 3 (Theorem 2) were obtained by A. G. Sergeev
Received: 04.04.2019
English version:
Transactions of the Moscow Mathematical Society, 2019, Volume 80, Pages 95–111
DOI: https://doi.org/10.1090/mosc/286
Bibliographic databases:
Document Type: Article
UDC: 517.9+534.7
MSC: 45G05, 92D30
Language: Russian
Citation: A. G. Sergeev, Kh. A. Khachatryan, “On the solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic”, Tr. Mosk. Mat. Obs., 80, no. 1, MCCME, M., 2019, 113–131; Trans. Moscow Math. Soc., 80 (2019), 95–111
Citation in format AMSBIB
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\by A.~G.~Sergeev, Kh.~A.~Khachatryan
\paper On the solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 1
\pages 113--131
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo619}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4082863}
\elib{https://elibrary.ru/item.asp?id=43303266}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 95--111
\crossref{https://doi.org/10.1090/mosc/286}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85083803624}
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    • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Trudy Moskovskogo Matematicheskogo Obshchestva
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