Geodesic
On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of $p$-adic strings
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 4, pp. 423-436

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The article considers a boundary value problem for a class of singular integral equations with an almost total-difference kernel and convex nonlinearity on the positive half-line. This problem arises in the dynamic theory of $ p $-adic open-closed strings. It is proved that any non-negative and bounded solution of a given boundary value problem is a continuous function and the difference between the limit and the solution is itself an integrable function on the positive half-line. For a particular case, it is proved that the solution is a monotonically non-decreasing function. A uniqueness theorem is established in the class of nonnegative and bounded functions. At the conclusion of the article, a specific applied example of this boundary problem is given.
Keywords: boundary value problem, convexity, continuity, summability, monotonicity
Mots-clés : solution limit. 
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     author = {Kh. A. Khachatryan and H. S. Petrosyan},
     title = {On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of $p$-adic strings},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {423--436},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a6/}
}
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Kh. A. Khachatryan; H. S. Petrosyan. On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of $p$-adic strings. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 4, pp. 423-436. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_4_a6/