Geodesic
On the solvability of a boundary value problem in $ p$-adic string theory
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 1, pp. 117-132.

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This paper is devoted to the study and solution of a boundary value problem for a convolution-type integral equation with cubic nonlinearity. The above problem has a direct application to the $ p$-adic theory of open-closed strings for the scalar tachyon field. It is shown that a one-parameter family of monotone continuous bounded solutions exists. Under additional conditions on the kernel of the equation, an asymptotic formula for the solutions thus constructed is established. Using these results, as particular cases we obtain Zhukovskaya's theorem on rolling solutions of the nonlinear equation in the $ p$-adic theory of open-closed strings and the Vladimirov–Volovich theorem on the existence of a nontrivial solution between certain vacua. The results are extended to the case of a more general nonlinear boundary value problem. 
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Kh. A. Khachatryan. On the solvability of a boundary value problem in $ p$-adic string theory. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 79 (2018) no. 1, pp. 117-132. http://geodesic.mathdoc.fr/item/MMO_2018_79_1_a2/

[1] L. V. Joukovskaya, “Iterative method for solving nonlinear integral equations describing rolling solutions in string theory”, Theoret. and Math. Phys., 146:3 (2006), 335–342 | DOI | DOI | MR | Zbl

[2] V. S. Vladimirov, “On the non-linear equation of a $p$-adic open string for a scalar field”, Russian Math. Surveys, 60:6 (2005), 1077–1092 | DOI | DOI | MR | Zbl

[3] V. S. Vladimirov, “Nonlinear equations for $p$-adic open, closed, and open-closed strings”, Theoret. and Math. Phys., 149:3 (2006), 1604–1616 | DOI | DOI | MR | Zbl

[4] Kh. A. Khachatryan, A. S. Petrosyan, A. A. Sisakyan, “O netrivialnoi razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa Urysona”, Tr. IMM UrO RAN, 23, no. 2, 2017, 266–273 | DOI

[5] V. S. Vladimirov, Ya. I. Volovich, “Nonlinear Dynamics Equation in p-Adic String Theory”, Theoret. and Math. Phys., 138:3 (2004), 297–309 | DOI | DOI | MR | Zbl

[6] I. Ya. Aref'eva, I. V. Volovich, “Cosmological daemon”, Journal of High Energy Physics, 2011, no. 8, 102 | DOI | Zbl

[7] A. N. Kolmogorov, V. S. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, 7-e izd., Fizmatlit, M., 2004, 572 pp.

[8] G. G. Gevorkyan, N. B. Engibaryan, “Novye teoremy dlya integralnogo uravneniya vosstanovleniya”, Izvestiya NAN Armenii, matematika, 32:1 (1997), 5–20 | Zbl

[9] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, v. 2, Fizmatlit, M., 1966, 800 pp.