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Ufimsk. Mat. Zh., 2010, Volume 2, Issue 2, Pages 102–117 (Mi ufa54)  

This article is cited in 3 scientific papers (total in 3 papers)

On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators

Kh. A. Khachatryan

Institute of Mathematics National Academy of Sciences, Yerevan, Armenia

Abstract: In present paper the classes of nonlinear integral equations with non completely continuous operators are considered.
It is assumed that conservative nonlinear operator of Wiener–Hopf-Hankell–Hammerstein type is a linear minorant to the initial Urysohn operator. The alternative theorems of the existence of positive solutions of above-mentioned class equations are proved. The asymptotic behavior of the obtained solutions at infinity is investigated. The article is finalized by the presentation of some examples arising in applications.

Keywords: Wiener–Hopf operator, eighen-value, limit of solution, one parameter family of positive solutions, asymptotic properties, Caratede'ory condition.

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Bibliographic databases:
UDC: 517.968
Received: 20.03.2010
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Citation: Kh. A. Khachatryan, “On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators”, Ufimsk. Mat. Zh., 2:2 (2010), 102–117

Citation in format AMSBIB
\Bibitem{Kha10}
\by Kh.~A.~Khachatryan
\paper On solvability of some classes of Urysohn nonlinear integral equations with noncompact operators
\jour Ufimsk. Mat. Zh.
\yr 2010
\vol 2
\issue 2
\pages 102--117
\mathnet{http://mi.mathnet.ru/ufa54}
\zmath{https://zbmath.org/?q=an:1240.45012}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Khachatryan Kh.A., “On a Class of Nonlinear Integral Equations with a Noncompact Operator”, J. Contemp. Math. Anal.-Armen. Aca., 46:2 (2011), 89–100  crossref  mathscinet  zmath  isi
    2. Kh. A. Khachatryan, “On a class of integral equations of Urysohn type with strong non-linearity”, Izv. Math., 76:1 (2012), 163–189  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Kh. A. Khachatryan, T. G. Sardaryan, “O razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa Urysona na vsei pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:1 (2017), 40–50  mathnet  crossref  elib
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