Abstract:
In this paper, we study the solvability of boundary value problems for integro-differential equation. One of the features of the equations under consideration is the possibility of degeneration when some of coefficients vanish. The other feature is that the equations under consideration are nonlocal. This motivates modifications in statement of problems. Nonlocal nature of equation in particular leads to nonlocal conditions. Sufficient conditions providing well-posedness of four problems are obtained.
Keywords:
integro-differential equations, boundary problems, degeneration, nonlocal conditions, existence and uniqueness of solutions.
Received: 28.09.2017
Bibliographic databases:
Document Type:
Article
UDC:
517.946
Language: Russian
Citation:
A. I. Kozhanov, “Boundary value problems for a class of nonlocal integro-differential equations with degeneration”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 4, 19–24
\Bibitem{Koz17}
\by A.~I.~Kozhanov
\paper Boundary value problems for a class of nonlocal integro-differential equations with degeneration
\jour Vestnik SamU. Estestvenno-Nauchnaya Ser.
\yr 2017
\issue 4
\pages 19--24
\mathnet{http://mi.mathnet.ru/vsgu558}
\crossref{https://doi.org/10.18287/2541-7525-2017-23-4-19-24}
\elib{https://elibrary.ru/item.asp?id=32274176}
Linking options:
https://www.mathnet.ru/eng/vsgu558
https://www.mathnet.ru/eng/vsgu/y2017/i4/p19
This publication is cited in the following 3 articles:
Nikolay Popov, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2528, “TOPICAL ISSUES OF THERMOPHYSICS, ENERGETICS AND HYDROGASDYNAMICS IN THE ARCTIC CONDITIONS”: Dedicated to the 85th Birthday Anniversary of Professor E. A. Bondarev, 2022, 020014
Aleksandr I. Kozhanov, “Nonlocal Integro-Differential Equations of the Second Order with Degeneration”, Mathematics, 8:4 (2020), 606
Nikolay S. Popov, AIP Conference Proceedings, 2035, 2018, 050014
Citation in format AMSBIB
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