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Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations

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References

  1. R. Courant & D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience, NY (1953).

    Google Scholar 

  2. M. G. Crandall & P. H. Rabinowitz: Nonlinear Sturm-Liouville eigenvalue problems and topological degree, J. Math. Mech. 19 (1970), 1083–1102.

    Google Scholar 

  3. A. Friedman: Partial Differential Equations, Holt, Rinehart and Winston, Inc. (1969).

  4. B. Gidas, W. M. Ni & L. Nirenberg: Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.

    Google Scholar 

  5. D. Gilbarg & N. S. Trudinger: Elliptic Partial Differential Equations of Second Order, 2nd Ed., Springer-Verlag (1983).

  6. M. Golubitsky, I. Stewart & D. G. Schaeffer, Singularities and Groups in Bifurcation, Theory Vol. II, Springer-Verlag (1988).

  7. T. J. Healey: Global bifurcation and continuation in the presence of symmetry with an application to solid mechanics, SIAM J. Math. Anal. 19 (1988), 824–840.

    Google Scholar 

  8. T. J. Healey: Symmetry and equivariance in nonlinear elastostatics, Part I. Arch. Rational Mech. Anal. 105 (1989), 205–228.

    Google Scholar 

  9. T. Kato: Perturbation Theory for Linear Operators, 2nd Ed., Springer-Verlag (1984).

  10. H. Kielhöfer: Multiple eigenvalue bifurcation for Fredholm operators, J. Reine Ang. Math. 358 (1985), 104–124.

    Google Scholar 

  11. J. K. Knowles: On finite anti-plane shear for incompressible elastic materials, J. Australian Math. Soc., Vol. XIX (Series B), 400–415 (1976).

    Google Scholar 

  12. J. Peetre: Another approach to elliptic boundary problems, Comm. Pure Appl. Math. Vol. XIV, 711–731 (1961).

    Google Scholar 

  13. P. H. Rabinowitz: Some global results for nonlinear eigenvalue problems, J. Functional Anal. 7 (1971) 487–513.

    Google Scholar 

  14. C. Scovel, I. G. Kevrekidis & B. Nicolaenko: Scaling laws and the prediction of bifurcations in systems modeling pattern formation, Physics Letters A 130 (1988), 73–80.

    Google Scholar 

  15. J. Serrin: A symmetry problem in potential theory, Arch. Rational Mech. Anal. 43 (1971), 304–318.

    Google Scholar 

  16. S. Smale: An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861–866.

    Google Scholar 

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Authors and Affiliations

  1. Department of Theoretical & Applied Mechanics and Center for Applied Mathematics, Cornell University, Ithaca, New York

    Timothy J. Healey & Hansjörg Kielhöfer

  2. Institut für Mathematik, Universität Augsburg, Germany

    Timothy J. Healey & Hansjörg Kielhöfer

Authors
  1. Timothy J. Healey
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  2. Hansjörg Kielhöfer
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Communicated by J. B. McLeod

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Healey, T.J., Kielhöfer, H. Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations. Arch. Rational Mech. Anal. 113, 299–311 (1991). https://doi.org/10.1007/BF00374696

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  • DOI: https://doi.org/10.1007/BF00374696

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