Skip to main content
SpringerLink
Log in

Asymptotic behavior of the eigenvalues of a boundary-value problem for a second-order elliptic operator-differential equation

  • Brief Communications
  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We study the asymptotic behavior of the eigenvalues of a boundary-value problem with spectral parameter in the boundary conditions for a second-order elliptic operator-differential equation. The asymptotic formulas for the eigenvalues 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

References

  1. J.-L. Lions and E. Magenes, Problemes aux Limites Non Homogenes et Applications, Dunod, Paris (1968).

    MATH  Google Scholar 

  2. V. I. Gorbachuk and M. A. Rybak, “On boundary-value problems for the Sturm-Liouville operator equation with spectral parameter both in the equation and in the boundary condition,” in: Direct and Inverse Scattering Problems [in Russian], Kiev (1981), pp. 3–13.

  3. M. A. Rybak, “On the asymptotic distribution of eigenvalues of some boundary-value problems for the Sturm-Liouville operator equation,” Ukr. Mat. Zh., 32, No. 2, 248–252 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  4. V. I. Gorbachuk and M. L. Gorbachuk, “On some boundary-value problems for the Sturm-Liouville equation with operator potential,” Ukr. Mat. Zh., 24, No. 3, 291–351 (1972).

    MathSciNet  MATH  Google Scholar 

  5. V. I. Gorbachuk and M. L. Gorbachuk, “On self-adjoint boundary-value problems with discrete spectrum generated by the Sturm-Liouville equation with unbounded operator coefficient,” Funk. Anal. Pril., 5, Issue 4, 67–68 (1971).

    Google Scholar 

  6. S. Yakubov and Ya. Yakubov, Differential-Operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall, Boca Raton (2000).

    MATH  Google Scholar 

  7. V. A. Il’in and A. F. Filippov, “On the character of spectrum of the self-adjoint extension of the Laplace operator in a bounded domain,” Dokl. Akad. Nauk SSSR, 191, No. 2, 267–269 (1970).

    MathSciNet  Google Scholar 

  8. S. Ya. Yakubov, “Boundary-value problem for the Laplace equation with nonclassical spectral asymptotics,” Dokl. Akad. Nauk SSSR, 265, No. 6, 1330–1333 (1982).

    MathSciNet  Google Scholar 

  9. B. A. Aliev, “Asymptotic behavior of the eigenvalues of a boundary-value problem for a second-order elliptic operator-differential equation with singular coefficient,” Differents. Uravn., 38, No. 1, 58–62 (2002).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Azerbaijan Academy of Sciences, Baku, Azerbaijan

    B. A. Aliev

Authors
  1. B. A. Aliev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1146–1152, August, 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aliev, B.A. Asymptotic behavior of the eigenvalues of a boundary-value problem for a second-order elliptic operator-differential equation. Ukr Math J 58, 1298–1306 (2006). https://doi.org/10.1007/s11253-006-0134-1

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0134-1

Keywords

Search

Navigation