INITIAL VALUE PROBLEM FOR A NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATION OF THIRD ORDER WITH A DEGENERATE KERNEL
DOI:
https://doi.org/10.52754/16948645_2024_2(5)_25Ачкыч сөздөр:
Initial value problem, third order integro-differential equation, unique solvability, real parameters, regular values, dependence on the parametersАннотация
In this paper, it is considered a third order nonlinear Fredholm integro-differential equations with initial value conditions and real parameters. A nonlinear functional-integral equations is derived. Theorem on a uniqueness and existence of the solution of the problem is proved for regular values of parameters. The method of compressing mapping in the space of continuous functions is applied. Continuous dependence on parameters of the solution of initial value problem is studied.
Библиографиялык шилтемелер
A. Anguraj, A. Vinodkumar, Global existence and stability results for partial delay integro-differential equations with random impulses, Filomat 37 (2023), No 1, 317-334. https://doi.org/10.2298/FIL2301317A
Zh. A. Artykova, R. A. Bandaliyev, and 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 (2023), No 10, 4215-4230. https://doi.org/10.1134/S1995080223100050
S. N. Askhabov, On a second-order integro-differential equation with difference kernels and power nonlinearity, Bulletin of the Karaganda University. Mathematics series 106 (2022), No 2, 38–48. DOI 10.31489/2022M2/38-48
A. T. Assanova, A two-point boundary value problem for a fourth order partial integro-differential equation, Lobachevskii Journal of Mathematics 42 (2021), No 3, 526-535. https://doi.org/10.1134/S1995080221030082
A. T. Assanova and S. N. Nurmukanbet, A solvability of a problem for a Fredholm integro-differential equation with weakly singular kernel, Lobachevskii Journal of Mathematics 43 (2022), No 1, 182-191. https://doi.org/10.1134/S1995080222040047
N. Aviltay and M. Akhmet, Asymptotic behavior of the solution of the integral boundary value problem for singularly perturbed integro-differential equations, Journal of Mathematics, Mechanics and Computer Science 112 (2021), No 4, 13–28. https://doi.org/10.26577/JMMCS.2021.v112.i4.02
A. Bellour and Kh. Rouiban, Iterative continuous collacation method for solving nonlinear Volterra integro-differential equations, Proceedings of the Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan 47 (2021), No 1, 99-111. https://doi.org/10.30546/2409-4994.47.1.99
V. F. Chistyakov and E. V. Chistyakova, Properties of degenerate systems of linear integro-differential equations and initial value problems for these equations, Differential Equations 59 (2023), No 1, 13-28. https://doi.org/10.1134/S0012266123010023
D. K. Durdiev and J. S. Safarov, Finding the two-dimensional relaxation kernel of an integro-differential wave equation, Diffential Equatations 59 (2023), No 2, 214-229. https://doi.org/10.1134/S0012266123020064
S. Iskandarov, Lower bounds for the solutions of a first-order linear homogeneous Volterra integro-differential equation, Differential. Equations 31 (1995), No 9, 1462-1466.
S. Iskandarov and G. T. Khalilov, On lower estimates of solutions and their derivatives to a fourth-order linear integro-differential Volterra equation, J. Math. Sci. (N. Y.) 230 (2018), No 5, 688-694.
N. A. Rautian and V. V. Vlasov, Spectral analysis of the generators for semigroups associated with Volterra integro-differential equations, Lobachevskii J. of Mathematics 44 (2023), No 3, 926-935.
Yu. G. Smirnov, On the equivalence of the electromagnetic problem of diffraction by an inhomogeneous bounded dielectric body to a volume singular integro-differential equation, Comput. Math. and Math. Physics 56 (2016), No 9, 1631-1640.
V. B. Vasilyev and Sh. H. Kutaiba, Asymptotic behavior of solution to some boundary value problem, Azerbaijan Journal of Mathematics 13 (2023), No 1, 51–61.
S. Yaghoubi, H. Aminikhaha, Kh. Sadri, An effective operational matrix method based on shifted sixth-kind Chebyshev polynomials for solving fractional integro-differential equations with a weakly singular kernel, Filomat 38 (2024), No 7, 2457-2486. https://doi.org/10.2298/FIL2407457Y
A. Yakar and H. Kutlay, Extensions of some differential inequalities for fractional integro-differential equations via upper and lower solutions, Bulletin of the Karaganda University. Mathematics series 109 (2023), No 1, 156-167. DOI 10.31489/2023M1/156-167
V. A. Yurko, Inverse problems for first-order integro-differential operators, Math. Notes 100 (2016), No 6, 876-882.
T. K. Yuldashev, Nonlocal inverse problem for a pseudohyperbolic-pseudoelliptic type integro-differential equations, Axioms 9 (2020), No 2, ID 45, 1-21. https://doi.org/10.3390/axioms9020045
T. K. Yuldashev, On a boundary value problem for a fifth order partial integro-differential equation, Azerbaijan Journal of Mathematics 12 (2022), No 2, 154-172.
T. K. Yuldashev, Z. K. Eshkuvatov and N. M. A. Nik Long, Nonlinear Fredholm functional-integral equation of first kind with degenerate kernel and integral maxima, Malaysian Journal of Fundamental and Applied Sciences 19 (2023), 82-92.
T. K. Yuldashev and A. K. Fayziyev, Inverse problem for a second order impulsive system of integro-differential equations with two redefinition vectors and mixed maxima, Nanosystems: Physics. Chemistry.Mathematics 14 (2023), No 1, 13-21. https://doi.org/10.17586/2220- 8054-2023-14-1-13-21
T. K. Yuldashev, and O. Sh. Kilichev, Inverse problem for a hyperbolic integro-differential equation with two redefinition conditions at the end of the interval and involution, Azerb. J. Math. 14 (2024), No 1, 3-22. https://doi.org/10.59849/2218-6816.2024.1.3
T. K. Yuldashev, F. D. Rakhmonov, On a Benney-Luke type differential equation with nonlinear boundary value conditions, Lobachevskii J. Math. 42 (2021), No 15, 3761-3772. https://doi.org/10.1134/S1995080222030210
G. V. Zavizion, Asymptotic solutions of systems of linear degenerate integro-differential equations, Ukr. Math. Journal, 55 (2003), No 4, 521-534.
T. K. Yuldashev and S. K. Zarifzoda, On a new class of singular integro-differential equations, Bulletin of the Karaganda University. Mathematics series 101 (2021), No 1, 138-148. https://doi.org/10.31489/2021M1/138-148
A. A. Boichuk and A. P. Strakh, Noetherian boundary-value problems for systems of linear integro-dynamical equations with degenerate kernel on a time scale, Nelineynye kolebaniya 17 (2014), No 1, 32-38. (in Russian)
D. S. Djumabaev and E. A. Bakirova, On one single solvability of boundary value problem for a system of Fredholm integro-differential equations with degenerate kernel, Nelineynye kolebaniya 18 (2015), No 4, 489-506. (in Russian)
T. K. Yuldashev, Mixed problem for pseudoparabolic integro-differential equation with degenerate kernel, Differential Equations 53 (2017), No 1, 99-108.
T. K. Yuldashev, Nonlocal mixed-value problem for a Boussinesq-type integro-differential equation with degenerate kernel, Ukrain. Math. J. 68 (2017), No. 8, 1278-1296.
T. K. Yuldashev, On a boundary value problem for a fifth order partial integro-differential equation, Azerb. J. Math. 12 (2022), No 2, 154-172.
T. K. Yuldashev, Inverse problem for a nonlinear Benney-Luke type integro-differential equations with degenerate kernel, Russian Math. (Izv. vuz) 60 (2016), No 8, 53-60.
T. K. Yuldashev, Inverse boundary-value problem for an integro-differential Boussinesq-type equation with degenerate kernel, Journal of Mathematical Sciences (N. Y.) 250 (2020), No 5, 847–858. https://doi.org/10.1007/s10958-020-05050-2
T. K. Yuldashev, Determining of coefficients and the classical solvability of a nonlocal boundary-value problem for the Benney-Luke integro-differential equation with degenerate kernel, J. of Math. Sci. (N. Y.) 254 (2021), No 6, 793-807 (2021).
T. K. Yuldashev, Yu. P. Apakov and A. Kh. Zhuraev, Boundary value problem for third order partial integro-differential equation with a degenerate kernel, Lobachevskii J. of Mathematics 42 (2021), No 6, 1317-1327.
T. K. Yuldashev, Zh. A. Artykova, and Sh. U. Alladustov, Nonlocal problem for a second order Fredholm integro-differential equation with degenerate kernel and real parameters, Proceedings of the Institute of Mathematics and Mechanics. National Academy of Sciences of Azerbaijan 49 (2023), No 2, 228-242. https://doi.org/10.30546/2409-4994.2023.49.2.228
Т. К. Юлдашев, Ж. А. Артыкова, “Об одной однородной нелокальной задаче для интегро-дифференциального уравнения Фредгольма второго порядка” // Вестник ОшГУ. Математика, Физика, Техника, 2023, № 1, 238-248 , https://doi.org.10.52754/16948645_2023_1_238
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Жарыяланды
Кандай шилтеме берүү керек
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Бөлүм
Лицензия
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