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Eurasian Math. J., 2012, Volume 3, Number 4, Pages 10–22 (Mi emj101)  

This article is cited in 9 scientific papers (total in 9 papers)

Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions

A. M. Akhtyamovab, V. A. Sadovnichyc, Ya. T. Sultanaevb

a Bashkir State University, Ufa, Russia
b Mavlutov Institute of Mechanics, Russian Academy of Sciences, Ufa, Russia
c M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: Inverse Sturm–Liouville problems and generalizations of Borg's uniqueness theorem to the case of general boundary conditions are considered. Chudov, Marchenko, Krein, Karaseva and authors' generalizations are adduced. New generalizations of Borg, Marchenko and Karaseva's uniqueness theorem to the case of nonseparated boundary conditions are obtained. Appropriate examples and counterexample are given.

Keywords and phrases: inverse eigenvalue problem, inverse Sturm–Liouville problem, nonseparated boundary conditions.

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Document Type: Article
MSC: 34A55, 34B05, 58C40
Received: 11.06.2012
Language: English

Citation: A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions”, Eurasian Math. J., 3:4 (2012), 10–22

Citation in format AMSBIB
\by A.~M.~Akhtyamov, V.~A.~Sadovnichy, Ya.~T.~Sultanaev
\paper Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions
\jour Eurasian Math. J.
\yr 2012
\vol 3
\issue 4
\pages 10--22

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    This publication is cited in the following articles:
    1. N. P. Bondarenko, “An inverse problem for the matrix quadratic pencil on a finite interval”, Eurasian Math. J., 4:3 (2013), 20–31  mathnet
    2. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “General Inverse Sturm-Liouville Problem With Symmetric Potential”, Azerbaijan J. Math., 5:2 (2015), 96–108  mathscinet  zmath  isi  elib
    3. Sadovnichii V.A., Sultanaev Ya.T., Akhtyamov A.M., “Solvability Theorems For An Inverse Nonself-Adjoint Sturm-Liouville Problem With Nonseparated Boundary Conditions”, Differ. Equ., 51:6 (2015), 717–725  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. A. Sadovnichy, Ya. T. Sultanaev, A. M. Akhtyamov, “On the solvability of inverse Sturm-Liouville problems with self-adjoint boundary conditions”, Dokl. Math., 93:1 (2016), 82–84  crossref  isi  elib  elib  scopus
    5. V. A. Sadovnichii, Ya. T. Sultanaev, A. M. Akhtyamov, “Uniqueness of reconstruction of the Sturm-Liouville problem with spectral polynomials in nonseparated boundary conditions”, Dokl. Math., 94:1 (2016), 461–463  crossref  mathscinet  zmath  isi  elib  scopus
    6. M. Akhymbek, N. Yessirkegenov, “Renovation of unknown coefficients of fixing and loading by the spectral data”, Applications of Mathematics in Engineering and Economics, AMEE'16, AIP Conf. Proc., 1789, eds. V. Pasheva, N. Popivanov, G. Venkov, Amer. Inst. Phys., 2016, UNSP 040003  crossref  isi  scopus
    7. B. Kanguzhin, N. Tokmagambetov, “A uniqueness theorem of a boundary inverse problem of a differential operator on an interval with integro-differential boundary conditions”, International conference on analysis and applied mathematics ICAAM 2016, AIP Conf. Proc., 1759, eds. A. Ashyralyev, A. Lukashov, Amer. Inst. Phys., 2016, UNSP 020046  crossref  isi  scopus
    8. A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Inverse problem for the diffusion operator with symmetric functions and general boundary conditions”, Eurasian Math. J., 8:1 (2017), 10–22  mathnet  isi
    9. A. A. Aitbaeva, A. M. Akhtyamov, “Determination of the type and parameters of a beam end fastening”, Azerbaijan J. Math., 7:1 (2017), 79–91  isi
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