ON SOLUTIONS OF SYSTEMS OF LINEAR INTEGRAL FREDHOLM EQUATIONS OF THE THIRD KIND WITH DEGENERATE MATRIX KERNELS ON THE SEMIAXIS
DOI:
https://doi.org/10.52754/16948645_2023_1_37Keywords:
решения, систем линейных интегральных уравнений, на полуоси, алгебраических, Фредгольма, третьего рода, эквивалентноAbstract
A system of Fredholm linear integral equations of the third kind with degenerate matrix kernels on semi-axes is investigated. The considered system of linear integral equations of the third kind belongs to the class of ill-posed problems. Based on a relatively new approach, it is shown that solutions for one class of systems of Fredholm linear integral equations of the third kind with degenerate matrix kernels on semi-axes are equivalent to solving systems of linear algebraic equations. Further, the questions of the existence and uniqueness of the solution for this system of linear integral equations of the third kind are studied.
References
Цалюк З.Б. В кн.: Итоги науки и техники. Сер. Матем. анализ, М., 1977, т.15, с.131-198.
Лаврентьев М.М. Об интегральных уравнениях первого рода // ДАН, 1959, т.127, №1, с.31-33.
Лаврентьев М.М., Романов В.Г., Шишатский С.П. Некорректные задачи математической физики и анализа. М.: Наука, 1980. 286 с.
Иманалиев М.И., Асанов А. О решениях систем нелинейных интегральных уравнений Вольтерра первого рода // ДАН, 1989, т.309, № 5, с.1052-1055.
Иманалиев М.И., Асанов А. Регуляризация и единственность решений систем нелинейных интегральных уравнений Вольтерра третьего рода. // ДАН, 2007, т.415, №1, с.14-17.
Иманалиев М.И., Асанов А. О решениях систем линейных интегральных уравнений Фредгольма третьего рода // ДАН, 2010, т.430, №6, с.1-4.
Иманалиев М.И., Асанов А. Асанов Р.А. Об одном классе систем линейных интегральных уравнений Фредгольма третьего рода // ДАН, 2011, т.437, № 5, с.592-596.
Apartsyn A.S. Nonclassical linear Volterra Equations of the First Kind. VSP, Utrecht, The Netherlands, 2003, 168 pages. DOI: https://doi.org/10.1515/9783110944976
Asanov A. Regularization, Uniqueness and Existence of Solutions of Volterra Equations of the First Kind. VSP, Utrecht, The Netherlands,1998, 276 pages. DOI: https://doi.org/10.1515/9783110943238
Avyt Asanov,Kalyskan Matanova, Ruhidin Asanov. A class of linear and nonlinear Fredholm integral equations of the third kind //Kuwait Journal of Science, 2017,Vol.44, No 1, pp.17-28.
Bukhgeim A.L. Volterra Equations and Inverse Problems. VSP, Utrecht, The Netherlands, 1999, 204 pages. DOI: https://doi.org/10.1515/9783110943245
Denisov A.M. Elements of the Theory of Inverse Problems. VSP, Utrecht, The Netherlands, 1999, 272 pages. DOI: https://doi.org/10.1515/9783110943252
Imanaliev M.I.,Asanov A. and Asanov R.A.,” Solutions to Systems of Linear Fredholm Integral Equations of the Third kind with Multipoint Singularities”//Doklady Mathematics, 2017, Vol. 95, No 3, pp. 235-239. DOI: https://doi.org/10.1134/S1064562417030140
Imanaliev M.I.,Asanov A. and Asanov R.A.,” On a class of Systems of Linear and Nonlinear Fredholm Integral Equations of the Third kind with Multipoint Singularities”// Differential Equations, 2018, Vol.54, No.3, pp. 381-391. DOI: https://doi.org/10.1134/S0012266118030096
Asanov A., Asanov R. A. One Class of Systems of Linear Fredholm Integral Equations of the Third Kind on the Real Line with Multipoint Singularities// Differential Equations, 2020, Vol. 56, pp. 1363–1370. DOI: https://doi.org/10.1134/S00122661200100122
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Journal of Osh State University. Mathematics. Physics. Technical Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
