Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Perturbed bifurcation theory

  • 320 Accesses

  • 99 Citations

References

  1. 1.

    Dean, E. T., & P. L.Chambré, Branching of solutions of some nonlinear eigenvalue problems. J. Math. Phys.11, 1567–1574 (1970).

  2. 2.

    Dean, E. T., & P. L.Chambré, On the solutions of the nonlinear eigenvalue problem 175-01. Bull. Amer. Math. Soc.76, 595–600 (1970).

  3. 3.

    Keener, J. P., Buckling imperfection sensitivity for columns and spherical caps. Quart. Appl. Math. (to appear).

  4. 4.

    Keener, J. P., Some modified bifurcation problems with application to imperfection sensitivity in buckling. Ph. D. thesis, California Institute of Technology, Pasadena, California 1972.

  5. 5.

    Keener, J. P., & H. B.Keller, Perturbed bifurcation and buckling of circular plates, Conference on Ordinary and Partial Differential Equations, University of Dundee. Lecture Notes in Mathematics280, 286–293. Berlin Heidelberg New York: Springer 1972.

  6. 6.

    Keener, J. P., & H. B.Keller, Positive solutions of convex nonlinear eigenvalue problems. J. Diff. Eqs. (to appear).

  7. 7.

    Keller, H. B., & W. F.Langfrod, Iterations, perturbations and multiplicities in nonlinear bifurcation problems. Arch. Rational Mech. Anal.43, 83–108 (1972).

  8. 8.

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

  9. 9.

    Laetsch, T. W., Eigenvalue problems for positive monotonic nonlinear operators. Ph. D. thesis, California Institute of Technology, Pasadena, California 1969.

  10. 10.

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

  11. 11.

    Vainberg, M. M., & V. A.Trenogin, The methods of Lyapunov and Schmidt in the theory of nonlinear equations and their further development. Russian Math. Surveys17, No. 2, 1–60 (1962).

  12. 12.

    Westreich, D., Bifurcation theory in a Banach space. Ph. D. thesis, Yeshiva Univ., New York City, N.Y. 1971.

  13. 13.

    Malkin, I. G., Some problems in the theory of nonlinear oscillations. State Pub. House of Tech. and Theory Lit., Moscow (1956); English translation AEC-tr-3766 (Book 1, Book 2), U.S. Dept. of Comm., N.B.S., Inst. for Applied Tech. 1959.

Download references

Author information

Additional information

This work was supported by the U.S. Army Research Office (Durham) under Contract CAHCO 4-68-C-0006 and by a fellowship from the Fannie and John Hertz Foundation.

Communicated by S.Antman

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Keener, J.P., Keller, H.B. Perturbed bifurcation theory. Arch. Rational Mech. Anal. 50, 159–175 (1973). https://doi.org/10.1007/BF00703966

Download citation

Keywords

  • Neural Network
  • Complex System
  • Nonlinear Dynamics
  • Electromagnetism
  • Bifurcation Theory