Geodesic
Solvability of some classes of nonlinear singular boundary value problems in the~theory of $p$-adic open--closed strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 1, pp. 106-117

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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, successive approximation, asymptotic behavior, uniqueness.
Mots-clés : kernel 
@article{TMF_2019_200_1_a5,
     author = {Kh. A. Khachatryan},
     title = {Solvability of some classes of nonlinear singular boundary value problems in the~theory of $p$-adic open--closed strings},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {106--117},
     publisher = {mathdoc},
     volume = {200},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_200_1_a5/}
}
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Kh. A. Khachatryan. Solvability of some classes of nonlinear singular boundary value problems in the~theory of $p$-adic open--closed strings. Teoretičeskaâ i matematičeskaâ fizika, Tome 200 (2019) no. 1, pp. 106-117. http://geodesic.mathdoc.fr/item/TMF_2019_200_1_a5/