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Matematicheskie Trudy, 2017, Volume 20, Number 2, Pages 193–205
DOI: https://doi.org/10.17377/mattrudy.2017.20.208 (Mi mt328) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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
Full-text PDF (202 kB) Citations (2)
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DOI: https://doi.org/10.17377/mattrudy.2017.20.208
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
Received: 16.01.2017
English version:
Siberian Advances in Mathematics, 2018, Volume 28, Issue 3, Pages 166–174
DOI: https://doi.org/10.3103/S1055134418030021
Bibliographic databases:
Document Type: Article
UDC: 517.968.4
Language: Russian
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
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\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{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85052498069}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические труды Siberian Advances in Mathematics
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    Full-text PDF :100
    References:80
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