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
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.
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Transactions of the Moscow Mathematical Society, 2018, 101–115
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
\paper On the solvability of a boundary value problem in $ p$-adic string theory
\serial Tr. Mosk. Mat. Obs.
\jour Trans. Moscow Math. Soc.
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