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 Trudy Inst. Mat. i Mekh. UrO RAN, 2018, Volume 24, Number 3, Pages 247–262 (Mi timm1566)

Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$

Kh. A. Khachatryana, H. S. Petrosyanb, M. H. Avetisyanc

a Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan
b National Agrarian University of Armenia
c Yerevan State University

Abstract: We study a class of nonlinear multidimensional integral equations of convolution type. This class of equations is directly applied in the p-adic theory of open-closed strings. We prove the existence of an n-parametric family of nontrivial continuous bounded solutions and establish certain properties of the constructed solutions: monotonicity in each argument, limit relations, and integral asymptotics. The solutions are used to study a nonlinear problem for the multidimensional heat equation. At the end of the paper we give example of such equations, which are of independent theoretical and practical interest.

Keywords: nontrivial solution, monotonicity, p-adic theory, limit, successive approximations.

 Funding Agency Grant Number State Committee on Science of the Ministry of Education and Science of the Republic of Armenia SCS 16YR-1A002 This work was supported by the Science Committee of the Ministry of Education and Science of Armenia (project no. SCS 16YR-1A002).

DOI: https://doi.org/10.21538/0134-4889-2018-24-3-247-262

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Bibliographic databases:

Document Type: Article
UDC: 517.968.4
MSC: 45G05

Citation: Kh. A. Khachatryan, H. S. Petrosyan, M. H. Avetisyan, “Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 247–262

Citation in format AMSBIB
\Bibitem{KhaPetAve18} \by Kh.~A.~Khachatryan, H.~S.~Petrosyan, M.~H.~Avetisyan \paper Solvability issues for a class of convolution type nonlinear integral equations in $\mathbb {R}^n$ \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2018 \vol 24 \issue 3 \pages 247--262 \mathnet{http://mi.mathnet.ru/timm1566} \crossref{https://doi.org/10.21538/0134-4889-2018-24-3-247-262} \elib{http://elibrary.ru/item.asp?id=35511291}