Skip to main content
Log in

On the asymptotic behavior of eigenvalues of the radial p-laplacian

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

We study the asymptotic behavior and distribution of the eigenvalues of the singular radial p-laplacian. We prove a Weyl type asymptotic formula for the number of eigenvalues less than a given value.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baouendi, M.S., Goulaouic, C.: Regularite et theorie spectrale pour une classe d’ operateurs elliptiques degeneres. Arch. Rat. Mech. Anal. 34, 361–379 (1969)

    Google Scholar 

  2. Courant, R., Hilbert, D.: Methods of Mathematical Physics. Vol 1, Interscience Publishers, Inc. New York, 1953

  3. Drabek, P., Manasevich, R.: On the Closed Solutions to some Nonhomogeneous Eigenvalue Problems with p-Laplacian. Diff. Int. Equations. 12, 773–788 (1999)

    Google Scholar 

  4. Fernandez Bonder, J., Pinasco, J.P.: Asymptotic Behavior of the Eigenvalues of the One Dimensional Weighted p-Laplace Operator. Arkiv för Mat. 41, 267–280 (2003)

    Google Scholar 

  5. Friedlander, L.: Asymptotic behaviour of eigenvalues of the p-Laplacian. Commun. Part. Diff. Eqs. 14 (8/9), 1059–1069 (1989)

    Google Scholar 

  6. Fučík, S., Nečas, J., Souček, J., Souček, V.: Spectral analysis of nonlinear operators. Lect. Notes in Math. Vol 346, Springer-Verlag, Berlin-Heidelberg-New York, 1973

  7. Garcia Azorero, J., Peral Alonso, I.: Existence and nonuniqueness for the p-laplacian: nonlinear eigenvalues. Commun. Partial Diff. Eq. 12, 1389–1430 (1987)

    Google Scholar 

  8. Pham The Lai: Comportement asymptotique du noyau de la resolvante et des valeurs propres d’ une classe d’ operateurs elliptiques degeneres non necesairement auto-adjoints. J. Math. Pures Appl. 55, 379–420 (1976)

    Google Scholar 

  9. Pinasco, J.P.: Comparison of Eigenvalues for the p-Laplacian with Integral Inequalities, Preprint, 2004

  10. Safarov, Yu., Vassiliev, D.: The asymptotic distribution of eigenvalues of partial differential operators. Transl. Math. Monogr. Vol. 155, Am. Math. Soc., Providence, R.I., 1998

  11. Walter, W.: Sturm-Liouville theory for the Radial Δ p -operator. Math. Z. 227, 175–185 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Juan P. Pinasco.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pinasco, J. On the asymptotic behavior of eigenvalues of the radial p-laplacian. manuscripta math. 117, 363–371 (2005). https://doi.org/10.1007/s00229-005-0567-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00229-005-0567-0

Keywords

Navigation