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.
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
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
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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
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\vol 80
\issue 1
\pages 113--131
\publ MCCME
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\jour Trans. Moscow Math. Soc.
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\crossref{https://doi.org/10.1090/mosc/286}
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https://www.mathnet.ru/eng/mmo619
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