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On the solvability of inverse Sturm–Liouville problems with self-adjoint boundary conditions

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Abstract

Theorems on the existence and uniqueness of a solution of the inverse Sturm–Liouville problem with self-adjoint nonseparated boundary conditions are proved. As spectral data two spectra and two eigenvalues are used. The theorems generalize the Levitan–Gasymov solvability theorem and Borg’s uniqueness theorem to the case of general boundary conditions.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    V. A. Sadovnichy

  2. Institute of Mechanics, Russian Academy of Sciences, ul. Karla Marksa 12, Ufa, 450025, Bashkortostan, Russia

    Ya. T. Sultanaev & A. M. Akhtyamov

  3. Bashkir State Pedagogical University, ul. Oktyabr’skoi revolyutsii 3a, Ufa, 450000, Bashkortostan, Russia

    Ya. T. Sultanaev

  4. Bashkir State University, ul. Zaki Validi 32, Ufa, 450074, Bashkortostan, Russia

    A. M. Akhtyamov

Authors
  1. V. A. Sadovnichy
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  2. Ya. T. Sultanaev
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  3. A. M. Akhtyamov
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Corresponding author

Correspondence to V. A. Sadovnichy.

Additional information

Original Russian Text © V.A. Sadovnichy, Ya.T. Sultanaev, A.M. Akhtyamov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 466, No. 5, pp. 526–528.

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Sadovnichy, V.A., Sultanaev, Y.T. & Akhtyamov, A.M. On the solvability of inverse Sturm–Liouville problems with self-adjoint boundary conditions. Dokl. Math. 93, 82–84 (2016). https://doi.org/10.1134/S1064562416010270

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  • DOI: https://doi.org/10.1134/S1064562416010270

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