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Perturbed bifurcation theory

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References

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

    Google Scholar 

  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).

    Google Scholar 

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

  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.

    Google Scholar 

  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.

    Google Scholar 

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

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  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).

    Google Scholar 

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

    Google Scholar 

  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.

    Google Scholar 

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Authors and Affiliations

  1. University of Arizona, 85721, Tucson, Arizona

    James P. Keener & Herbert B. Keller

  2. California Institute of Technology, 91109, Pasadena, California

    James P. Keener & Herbert B. Keller

Authors
  1. James P. Keener
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  2. Herbert B. Keller
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Additional information

Communicated by S.Antman

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.

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

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