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Regular Sturm-Liouville Operators with Integral Perturbation of Boundary Condition

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Functional Analysis in Interdisciplinary Applications (FAIA 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 216))

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Abstract

We are studying the issue of stability and instability of the basis property of the system of eigenfunctions and associated functions of the Sturm-Liouville operator with an integral perturbation of one boundary condition. This paper is devoted to a spectral problem for operator with an integral perturbation of boundary conditions, which are regular, but not strongly regular. We assume that the unperturbed problem has system of normalized eigenfunctions and associated functions which forms a Riesz basis. We construct a characteristic determinant of the spectral problem with an integral perturbation of the boundary conditions. The present work is the continuation of authors’ researchers on stability (instability) of basis property of root vectors of a differential operator with nonlocal perturbation of one of boundary conditions. The work includes a more detailed exposition of some previous results of authors in this directive, and there are given new results.

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Acknowledgements

The authors expresses his great gratitude to the academicians of NAS RK M. Otelbaev and T.Sh. Kal’menov for consistent support and fruitful discussion of the results. This research is supported by the grant no. 0825/GF4 and target program 0085/PTSF-14 of the Ministry of Education and Science of Republic of Kazakhstan.

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Authors and Affiliations

  1. South Kazakhstan State Pedagogical Institute, 16 G.Ilyev str., Shymkent, 160012, Kazakhstan

    Nurlan S. Imanbaev

  2. Institute of Mathematics and Mathematical Modeling, 125 Pushkin st., Almaty, 050010, Kazakhstan

    Makhmud A. Sadybekov

Authors
  1. Nurlan S. Imanbaev
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  2. Makhmud A. Sadybekov
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Corresponding author

Correspondence to Makhmud A. Sadybekov .

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Editors and Affiliations

  1. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Tynysbek Sh. Kalmenov

  2. Department of Mechanics and Mathematics, Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan

    Erlan D. Nursultanov

  3. Department of Mathematics, Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

  4. Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan

    Makhmud A. Sadybekov

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Imanbaev, N.S., Sadybekov, M.A. (2017). Regular Sturm-Liouville Operators with Integral Perturbation of Boundary Condition. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_21

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