This article is cited in 10 papers

Solvability of some classes of nonlinear singular boundary value problems in the theory of $p$-adic open–closed strings

Kh. A. Khachatryan

Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, Yerevan, Armenia

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 fields for open–closed strings as a particular case of the proved results.

Keywords: $p$-adic string, nonlinearity, kernel, successive approximation, asymptotic behavior, uniqueness.

Received: 19.12.2018
Revised: 30.01.2019

DOI: 10.4213/tmf9690

 English version: Theoretical and Mathematical Physics, 2016, 200:1, 1015–1025

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