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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». 2024. Vol 50

On an Integral Equation with Concave Nonlinearity

Author(s)
Khachatur A. Khachatryan1, Haykanush S. Petrosyan2

1Yerevan State University, Yerevan, Republic of Armenia

2Armenian National Agrarian University, Yerevan, Republic of Armenia

Abstract
A nonlinear integral equation on the semi-axis with a special substochastic kernel is studied. Such equations are encountered in the kinetic theory of gases when studying the nonlinear integro-differential Boltzmann equation within the framework of the nonlinear modified Bhatnagar-Gross-Crook model(BGC). Under certain restrictions on nonlinearity, it is possible to construct a positive continuous and bounded solution to this equation. Moreover, the uniqueness of the solution in the class of upper bounded on half-line functions having a positive infimum. It is also proved that the corresponding successive approximations converge uniformly at a rate of some geometric progression to the solution of the indicated equation. Under one additional condition, the asymptotic behavior of the solution at infinity is studied. At the end of the work, specific examples of these equations are given for which all the conditions of the proven facts are automatically met.
About the Authors

Khachatur A. Khachatryan, Dr. Sci. (Phys.-Math.), Prof., Yerevan State University, Yerevan, 0025, Republic of Armenia, khachatur.khachatryan@ysu.am

Haykanush S. Petrosyan, Cand. Sci. (Phys.Math.), Assoc. Prof., Agrarian University, Yerevan, 0009, Republic of Armenia, Haykuhi25@mail.ru

For citation

Khachatryan Kh. A., Petrosyan H. S. On an Integral Equation with Concave Nonlinearity. The Bulletin of Irkutsk State University. Series Mathematics, 2024, vol. 50, pp. 66–82. (in Russian)

https://doi.org/10.26516/1997-7670.2024.50.66

Keywords
concavity, iterations, monotonicity, convergence, asymptotics
UDC
517.968
MSC
45G05
DOI
https://doi.org/10.26516/1997-7670.2024.50.66
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