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Bulletin of Irkutsk State University. Series Mathematics, 2023, Volume 43, Pages 78–90
DOI: https://doi.org/10.26516/1997-7670.2023.43.78 (Mi iigum517) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Integro-differential equations and functional analysis

On the solution of Hammerstein integral equations with loads and bifurcation parameters

N. A. Sidorov, Lev Ryan D. Dreglea Sidorov

Irkutsk State University, Irkutsk, Russian Federation
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DOI: https://doi.org/10.26516/1997-7670.2023.43.78
Abstract: The Hammerstein integral equation with loads on the desired solution is considered. The equation contains a parameter for any value of which the equation has a trivial solution. Necessary and sufficient conditions are obtained for the coefficients of the equation and those values of the parameter (bifurcation points) in its neighborhood the equation has a nontrivial real solutions. The leading terms of the asymptotics of such branches of solutions are constructed. Examples are given illustrating the proven existence theorems.
Keywords: Hammerstein equation, branching, bifurcation points, asymptotics, loads.
Received: 10.11.2022
Revised: 06.12.2022
Accepted: 20.12.2022
Document Type: Article
UDC: 517.968.4
MSC: 45G10
Language: Russian
Citation: N. A. Sidorov, Lev Ryan D. Dreglea Sidorov, “On the solution of Hammerstein integral equations with loads and bifurcation parameters”, Bulletin of Irkutsk State University. Series Mathematics, 43 (2023), 78–90
Citation in format AMSBIB
\Bibitem{SidDre23}
\by N.~A.~Sidorov, Lev~Ryan~D.~Dreglea Sidorov
\paper On the solution of Hammerstein integral equations with loads and bifurcation parameters
\jour Bulletin of Irkutsk State University. Series Mathematics
\yr 2023
\vol 43
\pages 78--90
\mathnet{http://mi.mathnet.ru/iigum517}
\crossref{https://doi.org/10.26516/1997-7670.2023.43.78}
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