Abstract:
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, solution limit.
Citation:
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 S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 16:4 (2020), 423–436
\Bibitem{KhaPet20}
\by Kh.~A.~Khachatryan, H.~S.~Petrosyan
\paper On the qualitative properties of the solution of a nonlinear boundary value problem in the dynamic theory of $p$-adic strings
\jour Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr.
\yr 2020
\vol 16
\issue 4
\pages 423--436
\mathnet{http://mi.mathnet.ru/vspui468}
\crossref{https://doi.org/10.21638/11701/spbu10.2020.407}
Linking options:
https://www.mathnet.ru/eng/vspui468
https://www.mathnet.ru/eng/vspui/v16/i4/p423
This publication is cited in the following 3 articles:
Kh. A. Khachatryan, H. S. Petrosyan, “An iterative method for solving one class of non-linear integral equations
with Nemytskii operator on the positive semi-axis”, Izv. Math., 88:4 (2024), 760–793
Kh. A. Khachatryan, H. S. Petrosyan, “Constructive study of the solvability of one class of nonlinear integral equations with a symmetric kernel”, Siberian Adv. Math., 34:4 (2024), 320–336
H. S. Petrosyan, Kh. A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity
on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
Citation in format AMSBIB
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