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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 308, Pages 253–264
DOI: https://doi.org/10.4213/tm4051 (Mi tm4051) 		 
This article is cited in 13 scientific papers (total in 13 papers)

On the Solvability of a Class of Nonlinear Hammerstein–Stieltjes Integral Equations on the Whole Line

Kh. A. Khachatryanab, H. S. Petrosyanac

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
b Institute of Mathematics of National Academy of Sciences of the Republic of Armenia, Marshal Baghramian ave. 24/5, Yerevan, 0019, Republic of Armenia
c Armenian National Agrarian University, Teryan 74, Yerevan, 0009, Republic of Armenia
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DOI: https://doi.org/10.4213/tm4051
Abstract: We consider a nonlinear integral equation on the whole line with a Hammerstein–Stieltjes integral operator whose pre-kernel is a continuous distribution function. Under certain conditions imposed on the nonlinearity, we prove constructive existence and uniqueness theorems for nonnegative monotone bounded solutions. Some qualitative properties of the constructed solution are also studied. In particular, the results proved in the paper contain a theorem of O. Diekmann as a special case.
Keywords: pre-kernel, iterations, monotonicity, bounded solution, convergence.
Funding agency Grant number
Russian Science Foundation 19-11-00223
This work is supported by the Russian Science Foundation under grant 19-11-00223 and performed at Moscow State University.
Received: September 5, 2019
Revised: October 16, 2019
Accepted: October 21, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 308, Pages 238–249
DOI: https://doi.org/10.1134/S0081543820010198
Bibliographic databases:
Document Type: Article
UDC: 517.968.4
Language: Russian
Citation: Kh. A. Khachatryan, H. S. Petrosyan, “On the Solvability of a Class of Nonlinear Hammerstein–Stieltjes Integral Equations on the Whole Line”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 253–264; Proc. Steklov Inst. Math., 308 (2020), 238–249
Citation in format AMSBIB
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\paper On the Solvability of a Class of Nonlinear Hammerstein--Stieltjes Integral Equations on the Whole Line
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2020
\vol 308
\pages 253--264
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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    • This publication is cited in the following 13 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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