Solvability of Some Classes of Nonlinear Singular Boundary Value Problems in the Theory of p-Adic Open-Closed Strings

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.