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Trudy Moskovskogo Matematicheskogo Obshchestva, 2018, Volume 79, Issue 1, Pages 117–132 (Mi mmo610)  

This article is cited in 23 scientific papers (total in 23 papers)

On the solvability of a boundary value problem in $ p$-adic string theory

Kh. A. Khachatryan

Institute of Mathematics of the National Academy of Sciences of Armenia
References:
Abstract: This paper is devoted to the study and solution of a boundary value problem for a convolution-type integral equation with cubic nonlinearity. The above problem has a direct application to the $ p$-adic theory of open-closed strings for the scalar tachyon field. It is shown that a one-parameter family of monotone continuous bounded solutions exists. Under additional conditions on the kernel of the equation, an asymptotic formula for the solutions thus constructed is established. Using these results, as particular cases we obtain Zhukovskaya's theorem on rolling solutions of the nonlinear equation in the $ p$-adic theory of open-closed strings and the Vladimirov–Volovich theorem on the existence of a nontrivial solution between certain vacua.
The results are extended to the case of a more general nonlinear boundary value problem.
Key words and phrases: $p$-adic string, successive approximations, monotonicity, bounded solution, kernel, boundary value problem.
Received: 01.09.2017
English version:
Transactions of the Moscow Mathematical Society, 2018, Pages 101–115
DOI: https://doi.org/10.1090/mosc/281
Bibliographic databases:
Document Type: Article
UDC: 517.968.4
MSC: 45G05
Language: Russian
Citation: Kh. A. Khachatryan, “On the solvability of a boundary value problem in $ p$-adic string theory”, Tr. Mosk. Mat. Obs., 79, no. 1, MCCME, M., 2018, 117–132; Trans. Moscow Math. Soc., 2018, 101–115
Citation in format AMSBIB
\Bibitem{Kha18}
\by Kh.~A.~Khachatryan
\paper On the solvability of a boundary value problem in $ p$-adic string theory
\serial Tr. Mosk. Mat. Obs.
\yr 2018
\vol 79
\issue 1
\pages 117--132
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo610}
\elib{https://elibrary.ru/item.asp?id=37045085}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2018
\pages 101--115
\crossref{https://doi.org/10.1090/mosc/281}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85060867696}
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  • https://www.mathnet.ru/eng/mmo/v79/i1/p117
  • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Moskovskogo Matematicheskogo Obshchestva
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    Abstract page:1352
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    References:65
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