Skip to main content
SpringerLink
Log in

Nonlinear gradient operators and the method of lyapunov-schmidt

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

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

Bibliography

  1. Berger, M., A bifurcation theory for real solutions of nonlinear elliptic partial differential equations and related systems. Lecture VI in: Bifurcation Theory and Nonlinear Eigenvalue Problems by J. B. Keller & S. Antman, Courant Institute of Mathematical Sciences. New York University 1967.

  2. Berger, M., On nonlinear perturbations of the eigenvalues of a compact self-adjoint operator. Bull. A.M.S. 73, 704–708 (1967).

    Google Scholar 

  3. Cesari, L., Functional analysis and Galerkin's method. Michigan Math. J. 11, 385–414 (1964).

    Google Scholar 

  4. Cronin, J., Fixed Points and Topological Degree in Nonlinear Analysis. American Mathematical Society, Providence 1964.

    Google Scholar 

  5. Gustafson, K. & D. Sather, A branching analysis of the Hartree equation. Rend. Mat. (to appear).

  6. Knightly, G. & D. Sather, On nonuniqueness of solutions of the von Karman equations. Arch. Rational Mech. Anal. 36, 65–78 (1970).

    Google Scholar 

  7. Krasnosel'skii, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. New York: Pergamon Press 1964.

    Google Scholar 

  8. Krasnosel'skii, M. A., A. I. Perov, et al., Plane Vector Fields. New York: Academic Press 1966.

    Google Scholar 

  9. Rothe, E. H., Completely continuous scalars and variational methods. Ann. of Math. 49, 265–278 (1948).

    Google Scholar 

  10. Sather, D., Branching of solutions of an equation in Hubert space. Arch. Rational Mech. Anal. 36, 47–64 (1970).

    Google Scholar 

  11. Vainberg, M. M., & P. G. Aizengendler, The Theory and Methods of Investigation of Branch Points of Solutions. Progress in Mathematics, Volume 2, edited by R. V. Gamkrelidze. New York: Plenum Press 1968.

    Google Scholar 

  12. van der Waerden, B. L., Modern Algebra. Vol. II. New York: Frederick Ungar Publishing Company 1950.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Colorado, USA

    D. Sather

Authors
  1. D. Sather
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by H. Görtler

This research was supported in part by National Science Foundation Grant No. GP 19712 with the University of Colorado.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sather, D. Nonlinear gradient operators and the method of lyapunov-schmidt. Arch. Rational Mech. Anal. 43, 222–244 (1971). https://doi.org/10.1007/BF00251454

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00251454

Keywords

Search

Navigation