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.
Citation:
Kh. A. Khachatryan, H. S. Petrosyan, M. H. Avetisyan, “Solvability issues for a class of convolution type nonlinear integral equations in Rn”, Trudy Inst. Mat. i Mekh. UrO RAN, 24, no. 3, 2018, 247–262
\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{https://elibrary.ru/item.asp?id=35511291}
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https://www.mathnet.ru/eng/timm1566
https://www.mathnet.ru/eng/timm/v24/i3/p247
This publication is cited in the following 3 articles:
Kh. A. Khachatryan, A. S. Petrosyan, “O razreshimosti odnogo klassa nelineinykh dvumernykh integralnykh uravnenii tipa Gammershteina–Nemytskogo na ploskosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:3 (2023), 446–461
Kh. A. Khachatryan, H. S. Petrosyan, “Alternating bounded solutions of a class of nonlinear two-dimensional convolution-type integral equations”, Trans. Moscow Math. Soc., 82 (2021), 259–271
Kh. A. Khachatryan, H. S. Petrosyan, “On bounded solutions of a class of nonlinear integral equations in the plane and the Urysohn equation in a quadrant of the plane”, Ukr. Math. J., 73:5 (2021), 811–829
Citation in format AMSBIB
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