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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, Volume 28, Issue 3, Pages 284–292
DOI: https://doi.org/10.20537/vm180302
(Mi vuu639)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Comparison of solutions to boundary-value problems for linear functional-differential equations

E. S. Zhukovskiy, Kh. M. T. Takhir

Tambov State University named after G.R. Derzhavin, ul. Internatsional'naya, 33, Tambov, 392000, Russia
Full-text PDF (194 kB) Citations (1)
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Abstract: We consider the issues of solvability of boundary value problems for linear functional-differential equations. Statements allowing one to obtain conditions for the existence of a unique solution and for non-negativity of the Green's function, and to obtain a fundamental solution to the homogeneous equation are suggested. In order to apply these statements, one needs to define a “reference” boundary value problem that possesses the corresponding properties and to define an operator by means of the operators generated by the problem under study and the “reference” problem according to the given rule. If the spectral radius of this operator is less than 1, then the boundary value problem under consideration is uniquely solvable. Similarly, in order to obtain conditions for the nonnegativity of the Green's function and the fundamental solution, it is required to determine a special operator by the rule given in the paper and to verify its positivity. An example of application of the statements obtained to a particular boundary value problem with an integral boundary condition for the equation containing argument deviations to the unknown function and to its derivative is considered.
Keywords: linear functional-differential equation, boundary value problem, green's function, fundamental solution of a homogeneous equation, positive operator.
Funding agency Grant number
Russian Foundation for Basic Research 17-41-680975_р_а
16-01-00386_а
Ministry of Education and Science of the Russian Federation 3.8515.2017/БЧ
This work was supported by the Russian Foundation for Basic Research (projects no. 16-01-00386, no. 17-41-680975) and by the Ministry of Education and Science of the RF (project no. 3.8515.2017).
Received: 27.04.2018
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 34K10, 34K06
Language: Russian
Citation: E. S. Zhukovskiy, Kh. M. T. Takhir, “Comparison of solutions to boundary-value problems for linear functional-differential equations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:3 (2018), 284–292
Citation in format AMSBIB
\Bibitem{ZhuTak18}
\by E.~S.~Zhukovskiy, Kh.~M.~T.~Takhir
\paper Comparison of solutions to boundary-value problems for linear functional-differential equations
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 3
\pages 284--292
\mathnet{http://mi.mathnet.ru/vuu639}
\crossref{https://doi.org/10.20537/vm180302}
\elib{https://elibrary.ru/item.asp?id=35645982}
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  • This publication is cited in the following 1 articles:
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