Geodesic
Solvability of a~nonlinear integral equation in dynamical string
Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 44-53

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We investigate an integral equation of the convolution type with a cubic nonlinearity on the entire real line. This equation has a direct application in open-string field theory and in $p$-adic string theory and describes nonlocal interactions. We prove that there exists a one-parameter family of bounded monotonic solutions and calculate the limits of solutions constructed at infinity.
Keywords: bounded solution, iteration, monotonicity.
Mots-clés : nonlocal interaction, limit solution 
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     author = {A. Kh. Khachatryan and Kh. A. Khachatryan},
     title = {Solvability of a~nonlinear integral equation in dynamical string},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {44--53},
     publisher = {mathdoc},
     volume = {195},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a3/}
}
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A. Kh. Khachatryan; Kh. A. Khachatryan. Solvability of a~nonlinear integral equation in dynamical string. Teoretičeskaâ i matematičeskaâ fizika, Tome 195 (2018) no. 1, pp. 44-53. http://geodesic.mathdoc.fr/item/TMF_2018_195_1_a3/