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 Mat. Tr., 2017, Volume 20, Number 2, Pages 193–205 (Mi mt328)

On the solvability of one class of two-dimensional Urysohn integral equations

Kh. A. Khachatryan

Institute of Mathematics of the National Academy of Sciences of Armenia, Yerevan, Armenia

Abstract: We study one class of nonlinear Urysohn integral equations in a quadrant of the plane. It is assumed that, for the corresponding two-dimensional Urysohn operator, some Hammerstein operator with power nonlinearity serves as a minorant in the sense of M. A. Krasnosel'ski­ĭ. We prove the existence of a nonnegative (nontrivial) and bounded solution for such equations.

Key words: Urysohn equation, iteration, monotonicity, power nonlinearity, Carathéodory condition.

 Funding Agency Grant Number State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 16YR-1A002

DOI: https://doi.org/10.17377/mattrudy.2017.20.208

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English version:
Siberian Advances in Mathematics, 2018, 28:3, 166–174

UDC: 517.968.4

Citation: Kh. A. Khachatryan, “On the solvability of one class of two-dimensional Urysohn integral equations”, Mat. Tr., 20:2 (2017), 193–205; Siberian Adv. Math., 28:3 (2018), 166–174

Citation in format AMSBIB
\Bibitem{Kha17} \by Kh.~A.~Khachatryan \paper On the solvability of one class of two-dimensional Urysohn integral equations \jour Mat. Tr. \yr 2017 \vol 20 \issue 2 \pages 193--205 \mathnet{http://mi.mathnet.ru/mt328} \crossref{https://doi.org/10.17377/mattrudy.2017.20.208} \elib{http://elibrary.ru/item.asp?id=30558049} \transl \jour Siberian Adv. Math. \yr 2018 \vol 28 \issue 3 \pages 166--174 \crossref{https://doi.org/10.3103/S1055134418030021} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052498069} 

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This publication is cited in the following articles:
1. S. M. Andriyan, A. K. Kroyan, Kh. A. Khachatryan, “On solvability of class of nonlinear integral equations in $p$-adic string theory”, Ufa Math. J., 10:4 (2018), 12–23
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