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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 216, Number 1, Pages 184–200
DOI: https://doi.org/10.4213/tmf10401 (Mi tmf10401) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On nonlinear convolution-type integral equations in the theory of $p$-adic strings

A. Kh. Khachatryana, Kh. A. Khachatryanbc, H. S. Petrosyanac

a National Agrarian University of Armenia, Yerevan, Armenia
b Yerevan State University, Yerevan, Armenia
c Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10401
Abstract: We study a class of integral equations of convolution type on the whole line with a monotone and odd nonlinearity. We prove constructive existence and absence theorems for nonnegative (nontrivial) and bounded solutions. We study the asymptotic behavior of the constructed solution at $\pm\infty$. We also prove the uniqueness of the solution in the class of nonnegative (nonzero) and bounded functions and present specific examples of this class of equations that can be applied in various fields of mathematical physics.
Keywords: monotonicity, kernel, nonlinearity, nonnegative solution, convexity, convolution.
Funding agency Grant number
Ministry of Education, Science, Culture and Sports RA, Science Committee 21T-1A047
Russian Science Foundation 19-11-00223
The work of the first author was supported by the Science Committee of the Republic of Armenia (project No. 21T-1A047). The work of the second and third authors was supported by the Russian Science Foundation (grant No. 19-11-00223). The results in Secs. 1 and 4 were obtained by A. Kh. Khachatryan, and the results in Secs. 2 and 3, by Kh. A. Khachatryan and H. S. Petrosyan.
Received: 10.11.2022
Revised: 01.02.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 216, Issue 1, Pages 1068–1081
DOI: https://doi.org/10.1134/S0040577923070127
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On nonlinear convolution-type integral equations in the theory of $p$-adic strings”, TMF, 216:1 (2023), 184–200; Theoret. and Math. Phys., 216:1 (2023), 1068–1081
Citation in format AMSBIB
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\by A.~Kh.~Khachatryan, Kh.~A.~Khachatryan, H.~S.~Petrosyan
\paper On nonlinear convolution-type integral equations in the~theory
of $p$-adic strings
\jour TMF
\yr 2023
\vol 216
\issue 1
\pages 184--200
\mathnet{http://mi.mathnet.ru/tmf10401}
\crossref{https://doi.org/10.4213/tmf10401}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4619874}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2023TMP...216.1068K}
\transl
\jour Theoret. and Math. Phys.
\yr 2023
\vol 216
\issue 1
\pages 1068--1081
\crossref{https://doi.org/10.1134/S0040577923070127}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85165605182}
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    • This publication is cited in the following 1 articles:
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