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Contemporary Mathematics. Fundamental Directions, 2018, Volume 64, Issue 3, Pages 427–458
DOI: https://doi.org/10.22363/2413-3639-2018-64-3-427-458
(Mi cmfd356)
 

This article is cited in 4 scientific papers (total in 4 papers)

Inverse spectral problem for integrodifferential Sturm–Liouville operators with discontinuity conditions

S. A. Buterin

Saratov State University, Saratov, Russia
Full-text PDF (301 kB) Citations (4)
References:
Abstract: We consider the Sturm–Liouville operator perturbed by a convolution integral operator on a finite interval with Dirichlet boundary-value conditions and discontinuity conditions in the middle of the interval. We study the inverse problem of restoration of the convolution term by the spectrum. The problem is reduced to solution of the so-called main nonlinear integral equation with a singularity. To derive and investigate this equations, we do detailed analysis of kernels of transformation operators for the integrodifferential expression under consideration. We prove the global solvability of the main equation, this implies the uniqueness of solution of the inverse problem and leads to necessary and sufficient conditions for its solvability in terms of spectrum asymptotics. The proof is constructive and gives the algorithm of solution of the inverse problem.
Funding agency Grant number
Russian Science Foundation 17-11-01193
Document Type: Article
UDC: 517.984
Language: Russian
Citation: S. A. Buterin, “Inverse spectral problem for integrodifferential Sturm–Liouville operators with discontinuity conditions”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 64, no. 3, Peoples' Friendship University of Russia, M., 2018, 427–458
Citation in format AMSBIB
\Bibitem{But18}
\by S.~A.~Buterin
\paper Inverse spectral problem for integrodifferential Sturm--Liouville operators with discontinuity conditions
\inbook Proceedings of the Crimean autumn mathematical school-symposium
\serial CMFD
\yr 2018
\vol 64
\issue 3
\pages 427--458
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd356}
\crossref{https://doi.org/10.22363/2413-3639-2018-64-3-427-458}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Современная математика. Фундаментальные направления
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    Full-text PDF :125
    References:52
     
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