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Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2020, Volume 24, Number 4, Pages 644–662
DOI: https://doi.org/10.14498/vsgtu1790 (Mi vsgtu1790) 		 
Differential Equations and Mathematical Physics

On alternating and bounded solutions of one class of integral equations on the entire axis with monotonic nonlinearity

Kh. A. Khachatryanabc, H. S. Petrosyanad

a Lomonosov Moscow State University, Moscow, 119992, Russian Federation
b Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, 0019, Armenia
c Yerevan State University, Yerevan, 0025, Armenia
d National Agrarian University of Armenia, Yerevan, 0009, Armenia
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DOI: https://doi.org/10.14498/vsgtu1790
Abstract: The paper is devoted to the study of the existence and analysis of the qualitative properties of solutions for one class of integral equations with monotonic nonlinearity on the entire line. The indicated class of equations arises in the kinetic theory of gases. The constructive theorems of the existence of bounded solutions are proved, and certain qualitative properties of the constructed solutions are studied. At the end of the paper, specific applied examples of these equations are given.
Keywords: monotonicity, nonlinearity, kernel, convexity, limited solution.
Funding agency Grant number
Russian Science Foundation 19-11-00223
This work was supported by the Russian Foundation for Basic Research (project no. 19–11–00223).
Received: June 10, 2020
Revised: October 16, 2020
Accepted: November 16, 2020
First online: December 19, 2020
Bibliographic databases:
Document Type: Article
UDC: 517.968.74
MSC: 45G05
Language: Russian
Citation: Kh. A. Khachatryan, H. S. Petrosyan, “On alternating and bounded solutions of one class of integral equations on the entire axis with monotonic nonlinearity”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 24:4 (2020), 644–662
Citation in format AMSBIB
\Bibitem{KhaPet20}
\by Kh.~A.~Khachatryan, H.~S.~Petrosyan
\paper On alternating and bounded solutions of one class of~integral equations on~the entire axis with monotonic nonlinearity
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2020
\vol 24
\issue 4
\pages 644--662
\mathnet{http://mi.mathnet.ru/vsgtu1790}
\crossref{https://doi.org/10.14498/vsgtu1790}
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    		Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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