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Trudy Moskovskogo Matematicheskogo Obshchestva, 2018, Volume 79, Issue 1, Pages 117–132
(Mi mmo610)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/mmo610 https://www.mathnet.ru/eng/mmo/v79/i1/p117
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Abstract page: | 1352 | Full-text PDF : | 251 | References: | 65 | First page: | 3 |
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