Abstract:
We study classes of non-linear integral equations that have immediate
application to p-adic mathematical physics and to cosmology.
We prove existence and uniqueness theorems for non-trivial solutions
in the space of bounded functions.
Keywords:p-adic string, non-linear equation, iterations, monotonicity of a solution,
limit of a solution.
The work was financially supported by the State Committee of Science of the
Ministry of Education and Science of Armenia in the framework of Scientific
Project no. SCS 16YR-1A002.
Citation:
Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations
in p-adic string theory”, Izv. Math., 82:2 (2018), 407–427
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\by Kh.~A.~Khachatryan
\paper On the solubility of certain classes of non-linear integral equations
in $p$-adic string theory
\jour Izv. Math.
\yr 2018
\vol 82
\issue 2
\pages 407--427
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Linking options:
https://www.mathnet.ru/eng/im8580
https://doi.org/10.1070/IM8580
https://www.mathnet.ru/eng/im/v82/i2/p172
This publication is cited in the following 43 articles:
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “Solvability of a system of nonlinear integral equations on the entire line”, Complex Variables and Elliptic Equations, 2025, 1
A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “O konstruktivnoi razreshimosti odnogo klassa nelineinykh integralnykh uravnenii gammershteinovskogo tipa na vsei pryamoi”, Izv. vuzov. Matem., 2025, no. 3, 89–106
Kh. A. Khachatryan, H. S. Petrosyan, “On qualitative properties of the solution of a boundary value
problem for a system of nonlinear integral equations”, Theoret. and Math. Phys., 218:1 (2024), 145–162
A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya, otsutstviya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi s operatorom tipa Gammershteina — Ctiltesa”, Tr. IMM UrO RAN, 30, no. 1, 2024, 249–269
M. H. Avetisyan, Kh. A. Khachatryan, “On the Qualitative Properties of a Solution to a System of Infinite Nonlinear Algebraic Equations”, Sib Math J, 65:2 (2024), 455
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, “Asymptotic Behavior of the Solution for One Class of Nonlinear Integral Equations of Hammerstein Type on the Whole Axis”, J Math Sci, 282:2 (2024), 292
Kh. A. Khachatryan, H. S. Petrosyan, “On the Solvability of One Infinite System of Integral Equations with Power Nonlinearity on the Semi-Axis”, J. Contemp. Mathemat. Anal., 59:4 (2024), 305
Zahra Keyshams, Khachatur A. Khachatryan, Monire Mikaeili Nia, “Existence and Uniqueness Theorems for One Class of Hammerstein-type Nonlinear Integral Equations”, Lobachevskii J Math, 45:8 (2024), 3580
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
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On nonlinear convolution-type integral equations in the theory
of pp-adic strings”, Theoret. and Math. Phys., 216:1 (2023), 1068–1081
Kh. A. Khachatryan, H. S. Petrosyan, “On non-trivial solvability of one system of non-linear integral equations on the real axis”, Izv. Math., 87:5 (2023), 1062–1077
Kh. A. Khachatryan, H. S. Petrosyan, A. R. Hakobyan, “On solvability of one class of integral equations on whole line with monotonic and convex nonlinearity”, J. Math. Sci., 271:5 (2023), 610–624
A. Kh. Khachatryan, Kh. A. Khachatryan, “On qualitative properties of a solution of one class singular integral equations on the whole line with odd nonlinearity”, J. Math. Sci., 271:5 (2023), 597–609
Kh. A. Khachatryan, H. S. Petrosyan, “On the solvability of a system of nonlinear integral equations with the hammerstein–stieltjes operator on the half-line”, Diff Equat, 59:3 (2023), 383
Kh. A. Khachatryan, A. S. Petrosyan, “O razreshimosti odnogo klassa nelineinykh integralnykh uravnenii Gammershteina na poluosi”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 22:2 (2022), 169–179
Kh. A. Khachatryan, A. S. Petrosyan, “Asimptoticheskoe povedenie resheniya dlya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina na vsei pryamoi”, SMFN, 68, no. 2, Rossiiskii universitet druzhby narodov, M., 2022, 376–391
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022) (to appear)
Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 26:3 (2022), 446–479
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