On the solvability of a class of nonlinear integral equations in the problem of a spread of an epidemic
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A. G. Sergeev and Kh. A. Khachatryan
Translated by: the authors - Trans. Moscow Math. Soc. 2019, 95-111
- DOI: https://doi.org/10.1090/mosc/286
- Published electronically: March 31, 2020
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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.References
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Bibliographic Information
- Published electronically: March 31, 2020
- Additional Notes: 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 - © Copyright 2020 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2019, 95-111
- MSC (2010): Primary 45G05, 92D30
- DOI: https://doi.org/10.1090/mosc/286
- MathSciNet review: 4082862