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Tr. Mat. Inst. Steklova, 2020, Volume 308, Pages 253–264 (Mi tm4051)  

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

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.

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.


DOI: https://doi.org/10.4213/tm4051

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English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 308, 238–249

Bibliographic databases:

UDC: 517.968.4
Received: September 5, 2019
Revised: October 16, 2019
Accepted: October 21, 2019

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, Tr. 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 Tr. Mat. Inst. Steklova
\yr 2020
\vol 308
\pages 253--264
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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