Skip to main content
SpringerLink
Log in

Basis Properties in Lp of a Sturm-Liouville Operator with Spectral Parameter in the Boundary Conditions

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

The Sturm-Liouville operator with spectral parameter in the boundary conditions is considered, and sufficient conditions for the basis property of the system of eigenfunctions of this operator in the space Lp(0, 1), 1 < p < ∞, are obtained.

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

Similar content being viewed by others

References

  1. Walter, J., Regular eigenvalue problems with eigenvalue parameter in the boundary condition, Math. Z., 1973, vol. 133, no. 44, pp. 301–302.

    Article  MathSciNet  MATH  Google Scholar 

  2. Fulton, C.T., Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions, Proc. Roy. Soc. Edinburg Sect. A, 1977, vol. 77, no. 3–4, pp. 293–308.

    Google Scholar 

  3. Russakovskii, E.M., Operator treatment of boundary problems with spectral parameters entering via polynomials in the boundary conditions, Funct. Anal. Appl., 1975, vol. 9, no. 4, pp. 358–359.

    Article  Google Scholar 

  4. Kerimov, N.B. and Allakhverdiev, T.I., On a boundary value problem. I, Differ. Equations, 1993, vol. 29, no. 1, pp. 45–50.

    MATH  Google Scholar 

  5. Kerimov, N.B. and Allakhverdiev, T.I., On a boundary value problem. II, Differ. Equations, 1993, vol. 29, no. 6, pp. 814–821.

    MathSciNet  MATH  Google Scholar 

  6. Binding, P.A., Browne, P.J., and Seddighi, K., Sturm–Lioville problems with eigenparameter dependent boundary conditions, Proc. Edinb. Math. Soc. 1994, vol. 37, no. 1, pp. 57–72.

    Google Scholar 

  7. Kapustin, N.Yu. and Moiseev, E.I., Spectral problems with the spectral parameter in the boundary condition, Differ. Equations, 1997, vol. 33, no. 1, pp. 116–120.

    MathSciNet  MATH  Google Scholar 

  8. Kapustin, N.Yu., Oscillation properties of solutions to a non-self-adjoint spectral problem with spectral parameter in the boundary condition. Differ. Equations, 1999, vol. 35, no. 8, pp. 1031–1034.

    MathSciNet  MATH  Google Scholar 

  9. Kapustin, N.Yu. and Moiseev, E.I., The basis property in Lp of the system of eigenfunctions corresponding to two problems with a spectral parameter in the boundary condition, Differ. Equations, 2000, vol. 36, no. 10, pp. 1498–1501.

    Article  MathSciNet  MATH  Google Scholar 

  10. Moiseev, E.I. and Kapustin, N.Yu, On the singularities of the root space of a spectral problem with a spectral parameter in the boundary condition, Dokl. Math., 2002, vol. 66, no. 1, pp. 14–18.

    Google Scholar 

  11. Kerimov, N.B. and Mirzoev, V.S., On the basis properties of a spectral problem with a spectral parameter in a boundary condition, Sib. Math. J., 2003, vol. 44, no. 5, pp. 813–815.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kapustin, N.Yu., On a spectral problem arising in a mathematical model of torsional vibrations of a rod with pulleys at the ends, Differ. Equations, 2005, vol. 41, no. 10, pp. 1490–1492.

    Article  MathSciNet  MATH  Google Scholar 

  13. Kerimov, N.B. and Poladov, R.G., On basicity in Lp(0, 1) (1 < p < ∞) of the system of eigenfunctions of one boundary value problem. I, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 2005, vol. 22, no. 30, pp. 53–64.

    MathSciNet  MATH  Google Scholar 

  14. Kerimov, N.B. and Poladov, R.G., On basicity in Lp(0, 1) (1 < p < ∞) of the system of eigenfunctions of one boundary value problem. II, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 2005, vol. 23, no. 31, pp. 65–76.

    MathSciNet  MATH  Google Scholar 

  15. Aliev, Z.S., Basis properties of the root functions of an eigenvalue problem with a spectral parameter in the boundary conditions, Dokl. Math., 2010, vol. 82, no. 1, pp. 583–586.

    Article  MathSciNet  MATH  Google Scholar 

  16. Kerimov, N.B. and Poladov, R.G., Basis properties of the system of eigenfunctions in the Sturm–Liouville problem with a spectral parameter in the boundary conditions, Dokl. Math., 2012, vol. 85, no. 1, pp. 8–13.

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Khazar University, Baku, AZ1096, Azerbaijan

    N. B. Kerimov

Authors
  1. N. B. Kerimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. B. Kerimov.

Additional information

Russian Text © N.B. Kerimov, 2019, published in Differentsial’nye Uravneniya, 2019, Vol. 55, No. 2, pp. 148–157.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kerimov, N.B. Basis Properties in Lp of a Sturm-Liouville Operator with Spectral Parameter in the Boundary Conditions. Diff Equat 55, 149–158 (2019). https://doi.org/10.1134/S0012266119020010

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266119020010

Search

Navigation