T. K. Yuldashev, “On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 252–263; Comput. Math. Math. Phys., 59:2 (2019), 241

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2019, Volume 59, Number 2, Pages 252–263
DOI: https://doi.org/10.1134/S0044466919020169 (Mi zvmmf10833)

This article is cited in 37 scientific papers (total in 37 papers)

On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel

T. K. Yuldashev

Siberian State University of Science and Technology, Krasnoyarsk, 660014, Russia

Citations (37)

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DOI: https://doi.org/10.1134/S0044466919020169

Abstract: The problems of the existence and construction of solutions of a nonlocal boundary value problem for the homogeneous second-order Fredholm integrodifferential equation with a degenerate kernel and with two spectral parameters are considered. The singularities arising from the definition of arbitrary (unknown) constants are studied. The values of the spectral parameters are calculated and the solvability of the boundary value problem is established. The corresponding theorems are proven. Meaningful examples are provided.

Key words: integrodifferential equation, boundary value problem, degenerate kernel, solvability, spectral parameters.

Received: 10.10.2017

English version:
Computational Mathematics and Mathematical Physics, 2019, Volume 59, Issue 2, Pages 241–252
DOI: https://doi.org/10.1134/S0965542519020167

Bibliographic databases:

Document Type: Article

UDC: 517.968

Language: Russian

Citation: T. K. Yuldashev, “On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel”, Zh. Vychisl. Mat. Mat. Fiz., 59:2 (2019), 252–263; Comput. Math. Math. Phys., 59:2 (2019), 241–252

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This publication is cited in the following 37 articles:

A. N. Abdullozhonova, T. K. Yuldashev, A. K. Fayziyev, “Mixed Problem for an Impulsive Parabolic Integro-Differential Equation with Involution and Nonlinear Conditions”, Lobachevskii J Math, 45:3 (2024), 899
Zhazira Kadirbayeva, Elmira Bakirova, Agila Tleulessova, “Solving Fredholm integro-differential equations involving integral condition: A new numerical method”, Mathematica Slovaca, 74:2 (2024), 403
A. I. Egorov, “Properties of Solutions to Volterra-Type Integro-Differential Equations”, Lobachevskii J Math, 44:10 (2023), 4240
Kh. Khompysh, A. G. Shakir, “Inverse Problems for Kelvin–Voigt System with Memory: Global Existence and Uniqueness”, Lobachevskii J Math, 44:10 (2023), 4348
N. S. Imanbaev, “On a Spectral Problem for the Cauchy–Riemann Operator with Boundary Conditions of the Bitsadze–Samarskii Type”, Lobachevskii J Math, 44:3 (2023), 1162
A. T. Assanova, E. A. Bakirova, Zh. M. Kadirbayeva, “Two-Point Boundary Value Problem for Volterra–Fredholm Integro-Differential Equations and Its Numerical Analysis”, Lobachevskii J Math, 44:3 (2023), 1100
S. Iskandarov, A. T. Khalilov, “On Stability and Asymptotic Stability of Solutions for a Linear Fourth Order Volterra Integro-Differential Equation on the Half-Axis”, Lobachevskii J Math, 44:7 (2023), 2707
Zh. A. Artykova, R. A. Bandaliyev, T. K. Yuldashev, “Nonlocal Direct and Inverse Problems for a Second Order Nonhomogeneous Fredholm Integro-Differential Equation with Two Redefinition Data”, Lobachevskii J Math, 44:10 (2023), 4215
T. K. Yuldashev, Kh. Kh. Saburov, T. A. Abduvahobov, “Nonlocal problem for a nonlinear system of fractional order impulsive integro-differential equationswith maxima”, Chelyab. fiz.-matem. zhurn., 7:1 (2022), 113–122
A. T. Asanova, E. A. Bakirova, A. E. Imanchiev, “Kraevaya zadacha dlya integro-differentsialnogo uravneniya smeshannogo tipa”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 3–13
T. K. Yuldashev, B. Zh. Kadirkulov, “Ob odnom integro-differentsialnom uravnenii s drobnym operatorom Khilfera i nelineinymi maksimumami”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 83–95
T. K. Yuldashev, E. T. Karimov, “Ob odnom nagruzhennom integro-differentsialnom uravnenii smeshannogo tipa s drobnymi operatorami Gerasimova—Kaputo”, Geometriya, mekhanika i differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 211, VINITI RAN, M., 2022, 96–113
T. K. Yuldashev, T. G. Ergashev, T. A. Abduvahobov, “Nonlinear system of impulsive integro-differential equations with Hilfer fractional operator and mixed maxima”, Chelyab. fiz.-matem. zhurn., 7:3 (2022), 312–325
T. K. Yuldashev, O. Sh. Kilichev, “Nonlinear Inverse Problem for a Sixth Order Differential Equation with Two Redefinition Functions”, Lobachevskii J Math, 43:3 (2022), 804
Kairat I. Usmanov, Batirkhan Kh. Turmetov, Kulzina Zh. Nazarova, “On Unique Solvability of a Multipoint Boundary Value Problem for Systems of Integro-Differential Equations with Involution”, Symmetry, 14:8 (2022), 1626
M. T. Jenaliyev, M. T. Kosmakova, Zh. M. Tuleutaeva, “On the Solvability of Heat Boundary Value Problems in Sobolev Spaces”, Lobachevskii J Math, 43:8 (2022), 2133
Huizhen Qu, Jianwen Zhou, Tianwei Zhang, “Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations”, Mathematics, 10:13 (2022), 2204
T. K. Yuldashev, Z. K. Eshkuvatov, N. M. A. Nik Long, “Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima”, Math. Model. Comput., 9:1 (2022), 74
T. K. Yuldashev, A. K. Fayziyev, “Integral Condition with Nonlinear Kernel for an Impulsive System of Differential Equations with Maxima and Redefinition Vector”, Lobachevskii J Math, 43:8 (2022), 2332
A. A. Silaev, G. YU. Parshikova, A. A. Perfiliev, Lecture Notes in Networks and Systems, 397, Proceedings of the International Scientific Conference “Smart Nations: Global Trends In The Digital Economy”, 2022, 130

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