Skip to main content
SpringerLink
Log in

Identification of a polynomial in nonsplitting boundary conditions

  • Short Communications
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We prove criteria for the reconstructibility of n coefficients in nonsplitting boundary conditions of the Sturm-Liouville problem from n of its eigenvalues. We consider the corresponding applications, examples, and counterexamples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Shkalikov, A.A., Boundary Value Problems for Ordinary Differential Equations with a Parameter in the Boundary Conditions, Tr. Semin. im. I.G. Petrovskogo, 1983, no. 9, pp. 190–229.

  2. Kapustin, N.Yu. and Moiseev, E.I., On Spectral Problems with a Spectral Parameter in the Boundary Condition, Differ. Uravn., 1997, vol. 33, no. 1, pp. 115–119.

    MathSciNet  Google Scholar 

  3. Akhtyamov, A.M., On the Coefficients of Eigenfunction Expansions of Boundary Value Problems with a Parameter in the Boundary Conditions, Mat. Zametki, 2004, vol. 75, no. 4, pp. 493–506.

    Article  MathSciNet  Google Scholar 

  4. Benedek, A.I. and Panzone, R., On Inverse Eigenvalue Problems for a Second-Order Differential Equations with Parameter Contained in the Boundary Conditions, Notas Álgebra Anál., Bahía Blanca, Argentina, 1980, no. 9.

    Google Scholar 

  5. Chugunova, M.V., Inverse Spectral Problem for the Sturm-Liouville Operator with Eigenvalue Parameter Dependent on Boundary Conditions, Oper. Theory Adv. Appl., Basel, 2001, vol. 123, pp. 187–194.

    MathSciNet  Google Scholar 

  6. Van Der Mei, K. and Pivovarchik, V.N., An Inverse Sturm-Liouville Problem with Boundary Conditions Depending on the Spectral Parameter, Funktsional Anal. i Prilozhen., 2002, vol. 36, no. 4, pp. 74–77.

    MathSciNet  Google Scholar 

  7. Sadovnichii, V.A., Sultanaev, Ya.T., and Akhtyamov, A.M., An Inverse Problem for an Operator Pencil with Nonseparated Boundary Conditions, Dokl. Akad. Nauk, 2009, vol. 425, no. 1, pp. 31–33.

    MathSciNet  Google Scholar 

  8. Freiling, G. and Yurko, V., Inverse Problems for Sturm-Liouville Equations with Boundary Conditions Polynomially Dependent on the Spectral Parameter, Inverse Problems, 2010, vol. 26, pp. 1–17.

    Article  MathSciNet  Google Scholar 

  9. Akhtyamov, A.M., On the Determination of a Boundary Condition from a Finite Set of Eigenvalues, Differ. Uravn., 1999, vol. 35, no. 8, pp. 1127–1128.

    MathSciNet  Google Scholar 

  10. Akhtyamov, A.M. and Yamilova, L.S., Identification of Conditions of Closing a Conductor on the Basis of Fundamental Sequences of the Voltage of a Variable Current, Elektromagn. Volny Elektron. Sistemy, 2006, vol. 11, no. 2–3, pp. 15–17.

    Google Scholar 

  11. Naimark, M.A., Lineinye differentsial’nye operatory (Linear Differential Operators), Moscow: Nauka, 1969.

    Google Scholar 

  12. Kamke, E.W.H., Differentialgleichungen, Leipzig, 1959. Translated under the title Spravochnik po obyknovennym differentsial’nym uravneniyam, Moscow, 1981.

Download references

Author information

Authors and Affiliations

  1. Bashkir State University, Ufa, Russia

    A. M. Akhtyamov & R. R. Kumushbaev

Authors
  1. A. M. Akhtyamov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. R. Kumushbaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.M. Akhtyamov, R.R. Kumushbaev, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 11, pp. 1549–1552.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akhtyamov, A.M., Kumushbaev, R.R. Identification of a polynomial in nonsplitting boundary conditions. Diff Equat 48, 1527–1530 (2012). https://doi.org/10.1134/S0012266112110110

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266112110110

Keywords

Search

Navigation