Аннотация
The initial value problem of solvability and construction of solutions of a nonlinear Fredholm integro-differential equation of first order with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel in combination it with the method of regularization, we obtain an implicit functional-differential equation of first order with nonlinear maxima. We use initial boundary conditions to ensure the uniqueness of the solution. In order to use the method of a successive approximations and prove the one value solvability, we transform the obtained implicit functional-differential equation to the nonlinear Volterra type integro-differential equation with nonlinear maxima. The one value solvability of the problem is proved.
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Библиографические ссылки
Bakirova, E. A., Assanova, A. T., Kadirbayeva, Z. M. A problem with parameter for the integro-differential equations. Mathematical Modelling and Analysis, 2021. 26 (1), 34-54.
Efendiev M., Vougalter V. Solvability of some integro-differential equations with drift. Osaka J. Math. 2020. 57, 247-265.
El-Sayeda A.M.A., Aahmedb R.G., Solvability of the functional integro-differential equationwith self-reference and state-dependence. Journal of Nonlinear Sciences and Applications. 2020. 13. p. 1-8.
Sidorov N., Sidorov D., Dreglea A., Solvability and bifurcation of solutions of nonlinear equations with Fredholm operator. Symmetry. 2020. 12 (6), ID 920, 1-21.
Rojas E.M., Sidorov N.A., Sinitsyn A.V, A boundary value problem for noninsulated magnetic regime in a vacuum diode. Symmetry. 2020. 12 (4), ID 617 14 pp.
Zhang Y. Solvability of a class of integro-differential equations and connections to one-dimensional inverse problems. Journal of Mathematical Analysis and Applications. 2006. Vol. 321, Iss.1, p. 286-298.
Falaleev M.V., Fundamental operator-valued functions of singular integrodifferential operators in Banach spaces, J. Math. Sciences. 2018. 230 (5). P. 782-785.
Falaleev M.V., Orlov S.S., Degenerate integro-differential operators in Banach spaces and their applications. Russian Math. (Iz. VUZ). 2011. 55 (10). P. 59-69.
Assanova A. T., Bakirova E. A. and Kadirbayeva Z. M. Numerical solution to a control problem for integro-differential equations, Comput. Math. and Math. Phys., 2020. Vol. 60. No. 2. P. 203-221.
Dzhumabaev D. S., New general solutions to linear Fredholm integro-differential equations and their applications on solving the boundary value problems. Journal of Computational and Applied Mathematics, Vol. 327, No. 1. (2018), 79-108
Dzhumabaev D. S., Mynbayeva S. T., New general solution to a nonlinear Fredholm integro-differential equation. Eurasian Math. J., Vol. 10, No. 4. (2019), 24-33
Dzhumabaev D. S., Mynbayeva S. T., One approach to solve a nonlinear boundary value problem for the Fredholm integro-differential equation. Bulletin of the Karaganda university-Mathematics, Vol. 97, No. 1. (2020), 27-36
Dzhumabaev D. S., Zharmagambetov A. S., Numerical method for solving a linear boundary value problem for Fredholm integro-differential equations. News of the National Academy of Sciences of the Republic of Kazakhstan-Series Physico-Mathematical, Vol. 2(312). (2017), 5-11
Yuldashev T. K., Nonlocal mixed-value problem for a Boussinesq-type integrodifferential equation with degenerate kernel. Ukrainian Mathematical Journal. Vol. 68, No. 8. (2016), 1278-1296
Yuldashev T. K., Mixed problem for pseudoparabolic integrodifferential equation with degenerate kernel. Differential equations. Vol. 53, No. 1. (2017), 99-108
. Yuldashev T. K., Determination of the coefficient and boundary regime in boundary value problem for integro-differential equation with degenerate kernel. Lobachevskii journal of mathematics, Vol. 38, No. 3, (2017), 547-553
Yuldashev T. K., Nonlocal boundary value problem for a nonlinear Fredholm integro-differential equation with degenerate kernel. Differential equations. Vol. 54, No. 12. (2018), 1646-1653
Yuldashev T. K., Spectral features of the solving of a Fredholm homogeneous integro-differential equation with integral conditions and reflecting deviation. Lobachevskii Journal of Mathematics. Vol. 40, No. 12 (2019), 2116-2123
Yuldashev T. K., On the solvability of a boundary value problem for the ordinary Fredholm integrodifferential equation with a degenerate kernel. Computational Mathematics and Math. Physics, Vol. 59. No. 2. (2019), 241-252 ,
Yuldashev T. K., On a boundary-value problem for a fourth-order partial integro-differential equation with degenerate kernel. Journal of Mathematical Sciences. Vol. 245, No. 4. (2020), 508-523,
Imanaliev M.I., Asanov A. Regularization, Uniqueness and Existence of Solution for Volterra Integral Equations of First Kind. Studies by Integro-Diff. Equations. Vol. 21. Frunze, Ilim, 1988. P. 3-38 [in Russian]
. Lavrent'ev M.M., Romanov V.G., Shishatskii S.R. Noncorrect problems of mathematical physics and analysis. Moscow, Science, 1980 [in Russian]
Mamatov, J., & Parmonov, A. (2020). Tasvirli masala matematikani o'qitish samaradorligini oshirish vositasi sifatida. Архив Научных Публикаций JSPI, 109-109.
Mamatov, J. (2020). Tasvirli masalalar tuzishda yo'l qo'yiladigan kamchiliklarni yop'qotish haqida. Архив Научных Публикаций JSPI.
Mamatov, J., Qahhorov, M. ., Parmanov, A. ., & Fayzullaev, S. . (2021). ABOUT THE MAIN TASKS OF TEACHING GEOMETRY AT THE SECONDARY SCHOOL. Журнал математики и информатики, 1(1). извлечено от https://matinfo.jspi.uz/index.php/matinfo/article/view/1239
Mamatov, J. (2020). Matematika fanini o’qitishda shaxsga yo’naltirish va kasbiy faoliyatga yo'naltirishning pedagogik shartlari. Журнал математики и информатики, (1).
Mamatov, J., & Tursunov , M. (2021). PIRAMIDALAR VA ULARNING TEKISLIKLAR BILAN KESIMI. Журнал математики и информатики, 1(2). извлечено от https://matinfo.jspi.uz/index.php/matinfo/article/view/1212
Mamatov, J. (2021). PRIZMALAR VA ULARNING TEKISLIKLAR BILAN KESIMI. Журнал математики и информатики, 1(2). извлечено от https://matinfo.jspi.uz/index.php/matinfo/article/view/1211
Mamatov, J., & Parmanov, A. (2021). PLANIMETRIK MASALALARNI ZAMONAVIY AXBOROT TEXNOLOGIYALARI VOSITASIDA O’QITISHNING SAMARADORLIGI HAQIDA . Журнал математики и информатики, 1(2). извлечено от https://matinfo.jspi.uz/index.php/matinfo/article/view/1702
Mamatov, J., & Parmanov, A. (2021). “3D CABRILOG V 2” DASTURI VOSITASIDA O’QUVCHILAR FAZOVIY TASAVVURINI RIVOJLANTIRISH . Журнал математики и информатики, 1(2). извлечено от https://matinfo.jspi.uz/index.php/matinfo/article/view/1703
Авторы
Tursun Yuldashev
National University of Uzbekistan
Klara Holmanova
Jizzakh State Pedagogic Institute
Ключевые слова:
Integro-differential equation, first order, nonlinear functional-differential equation, degenerate kernel, nonlinear maxima, regularization, one value solvabilityВыпуск
Раздел: Articles
