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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 10–14
DOI: https://doi.org/10.31857/S2686954322700023 (Mi danma310) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Integro-differential equation with a sum-difference kernels and power nonlinearity

S. N. Askhabovabc

a Chechen State Pedagogical University, Grozny, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
c Kadyrov Chechen State University, Grozny, Russia
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DOI: https://doi.org/10.31857/S2686954322700023
Abstract: Sharp a priori estimates are obtained for solutions to a nonlinear Volterra-type integro-differential equation with a sum-difference kernel in a cone of the space of functions continuous on the positive half-axis. On the basis of these estimates, the method of weighted metrics is used to prove a global theorem on the existence, uniqueness, and a method of finding a nontrivial solution of the indicated equation. It is shown that this solution can be found by a method of successive approximations of the Picard type, and an estimate is given for the rate of their convergence in terms of the weighted metric. Conditions under which only the trivial solution exists are indicated. Examples are given to illustrate the results.
Keywords: Volterra integro-differential equation, sum-difference kernel, power nonlinearity.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FEGS-2020-0001
Russian Science Foundation 22-11-00177
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (subject code FEGS-2020-0001) in the part concerning the derivation of sharp a priori estimates for the solution of a nonlinear integro-differential equation with a sum-difference kernel. The rest of this work was supported by the Russian Science Foundation, grant no. 22-11-00177.
Presented: A. L. Semenov
Received: 06.10.2022
Revised: 10.10.2022
Accepted: 17.10.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3, Pages 412–415
DOI: https://doi.org/10.1134/S1064562422700065
Bibliographic databases:
Document Type: Article
UDC: 517.968.4
Language: Russian
Citation: S. N. Askhabov, “Integro-differential equation with a sum-difference kernels and power nonlinearity”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 10–14; Dokl. Math., 106:3 (2022), 412–415
Citation in format AMSBIB
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\by S.~N.~Askhabov
\paper Integro-differential equation with a sum-difference kernels and power nonlinearity
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 507
\pages 10--14
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\crossref{https://doi.org/10.31857/S2686954322700023}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4563838}
\elib{https://elibrary.ru/item.asp?id=49991276}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 3
\pages 412--415
\crossref{https://doi.org/10.1134/S1064562422700065}
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