Abstract
We investigate boundary value problems for a singular integral equation of the convolution type with a power-law nonlinearity. Such problems arise in the theory of p-adic open-closed strings. We prove constructive theorems on the existence of nontrivial solutions and also prove a uniqueness theorem in a certain weight class of functions. We study asymptotic properties of the constructed solutions and obtain the Vladimirov theorem on tachyon Gelds for open-closed strings as a particular case of the proved results.
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The author thanks the referee for the useful comments.
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This research was supported by the GKN MON RA (Project No. SCS 18T-1A004).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 1, pp. 106–117, July, 2019.
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Khachatryan, K.A. Solvability of Some Classes of Nonlinear Singular Boundary Value Problems in the Theory of p-Adic Open-Closed Strings. Theor Math Phys 200, 1015–1025 (2019). https://doi.org/10.1134/S0040577919070067
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DOI: https://doi.org/10.1134/S0040577919070067