Solvability criterion of linear boundary-value problems for integro-differential Fredholm equations with a degenerate kernel in Banach spaces
Abstract
UDC 517.983
Using the theory of generalized inversion of operators and integral operators, we obtain a criterion for solvability and a general form of solutions of linear boundary-value problem for integro-differential equation with a degenerate kernel in Banach space.
References
N. N. Vassiliev, I. N. Parasidis, E. Providas, Exact solution method for Fredholm integro-differential equations with multipoint and integral boundary conditions, Part 1. Extension method, Informaczionno-upravlyayushhie sistemy`, № 6, 14 – 23 (2018). DOI: https://doi.org/10.31799/1684-8853-2018-6-14-23
Gupta Vidushi, Dabas Jaydev, Existence results for a fractional integro-differential equation with nonlocal boundary conditions and fractional impulsive conditions, Nonlinear Dynamics and Syst. Theory, 15, № 4, 370 – 382 (2015).
K. D. Tsilika, An exact solution method for Fredholm integro-differential equations, Informaczionno-upravlyayushhie sistemy, № 4, 2 – 8 (2019). DOI: https://doi.org/10.31799/1684-8853-2019-4-2-8
D. S. Dzhumabaev, E. A. Bakirova, Criteria for the unique solvability of a linear two-point boundary-value problem for systems of integro-differential equations, Different. Equat., 49, № 9, 914 – 937 (2013), https://doi.org/10.1134/S0012266113090048 DOI: https://doi.org/10.1134/S0012266113090048
M. Turkyilmazoglu, An effective approach for numerical solutions of high-order Fredholm integro-differential equations, Appl. Math. and Comput., 227 , 384 – 398 (2014), https://doi.org/10.1016/j.amc.2013.10.079 DOI: https://doi.org/10.1016/j.amc.2013.10.079
I. M. Cherevko, I. V. Yakimov, Chislenny`j metod resheniya kraevy`kh zadach dlya integrodifferenczial`ny`kh uravnenij s otklonyayushhimsya argumentom, Ukr. mat. zhurn., 41, № 6, 854 – 860 (1989).
Kumar Pradeep, Haloi Rajib, D. Bahuguna, D. N. Pandey, Existence of solutions to a new class of abstract noninstantaneous impulsive fractional integro-differential equations, Nonlinear Dynamics and Syst. Theory, 16, № 1, 73 – 85 (2016).
M. V. Falaleev, Integro-differenczial`ny`e uravneniya s fredgol`movy`m operatorom pri starshej proizvodnoj v banakhovy`kh prostranstvakh i ikh prilozheniya, Izv. Irkut. gos. un-ta. Matematika, vy`p. 2, 90 – 102 (2012).
Yu. K. Lando, Ob indekse i normal`noj razreshimosti integro-differenczial`ny`kh operatorov, Differencz. rivnyannya, 4, № 6, 1112 – 1126 (1968).
Yu. L. Daletskiĭ, M. G. Kreĭn, Ustojchivost` reshenij differenczial`ny`kh uravnenij v banakhovom prostranstve, Nauka, Moskva (1970).
A. M. Samoilenko, A. A. Boichuk, V. F. Zhuravlev, Linear boundary value problems for normally solvable operator equations in a banach space, Different. Equat., 50, № 3, 1 – 11 (2014), https://doi.org/10.1134/S0012266114030057 DOI: https://doi.org/10.1134/S0012266114030057
A. A. Boichuk, V. F. Zhuravlev, Solvability criterion of integro-differential equations with degenerate kernel in Banach spaces, Nonlinear Dynamics and Systems Theory, 18, № 4, 331 – 341 (2019), https://doi.org/10.1007/s42330-018-0034-z DOI: https://doi.org/10.1007/s42330-018-0034-z
A. A. Boichuk, V. F. Zhuravlev, A. M. Samoilenko, Normal`no razreshimy`e kraevy`e zadachi, Nauk. dumka, Kiev (2019).
M. M. Popov, Dopovnyuval`ni prostori i deyaki zadachi suchasnoyi geometriyi prostoriv Banakha, Matematika s`ogodni'07, vip. 13, 78 – 116 (2007).
V. P. Zhuravl’ov, Generalized inversion of fredholm integral operators with degenerate kernels in Banach spaces, J. Math. Sci., 212, № 3, 275 – 289 (2016).
V. F. Zhuravlev, N. P. Fomin, P. N. Zabrodskij, Usloviya razreshimosti i predstavlenie reshenij uravnenij s operatorny`mi matriczami v banakhovy`kh prostranstvakh, Ukr. mat. zhurn., 71, № 4, 471 – 485 (2019).
S. G. Kreĭn, Linear equations in a Banach space, Izdat. ``Nauka, Moscow, (1971).
V. F. Zhuravlev, Kriterij razreshimosti i predstavlenie reshenij linejny`kh n- (d)-normal`ny`kh operatorny`kh uravnenij v banakhovom prostranstve, Ukr. mat. zhurn., 62, № 2, 167 – 182 (2010).
A. M. Samoilenko, O. A. Boichuk, S. A. Krivosheya, Krajovi zadachi dlya sistem linijnikh integro-diferenczial`nikh rivnyan` z virodzhenim yadrom, Ukr. mat. zhurn., 48, № 11, 1576 – 1579 (1996).
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