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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2023. Vol 43

On the Solution of Hammerstein Integral Equations with Loads and Bifurcation Parameters

Author(s)
Nikolai A. Sidorov1, Lev Ryan D. Dreglea Sidorov1

1Irkutsk State University, Irkutsk, Russian Federation

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
About the Authors

Nikolai A. Sidorov, Dr. Sci. (Phys.–Math.), Prof., Irkutsk State University, Irkutsk, 664003, Russian Federation, sidorov@math.isu.runnet.ru

Lev Ryan D. Dreglea Sidorov, student, Irkutsk State University, Irkutsk, 664033, Russian Federation, lev.ryan.lev@gmail.com

For citation
Sidorov N.A., Dreglea Sidorov L.R.D. On the Solution of Hammerstein Integral Equations with Loads and Bifurcation Parameters. The Bulletin of Irkutsk State University. Series Mathematics, 2023, vol. 43, pp. 78–90. (in Russian) https://doi.org/10.26516/1997-7670.2023.43.78
Keywords
Hammerstein equation, branching, bifurcation points, asymptotics, loads.
UDC
517.968.4
MSC
45G10
DOI
https://doi.org/10.26516/1997-7670.2023.43.78
References
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  9. Sidorov N.A., Sidorov D.N. Nonlinear Volterra Equations with Loads and Bifurcation Parameters: Existence Theorems and Construction of Solutions. Differantial Equations, 2021, vol. 57, pp. 1640–1651. https://doi.org/10.1134/S0012266121120107
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Full text (russian)