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Bifurcation, perturbation of simple eigenvalues, itand linearized stability

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References

  1. Agmon, S., A. Douglis, & L. Niremberg, Estimates near the boundary for solutions of partial elliptic differential equations satisfying general boundary conditions, I. Comm. Pure Appl. Math. 12, 623–727 (1959)

    Google Scholar 

  2. Amann, H., Existence of multiple solutions for nonlinear elliptic boundary value problems. Indiana Univ. Math. J. (to appear)

  3. Amann, H., On the existence of positive solutions of nonlinear elliptic boundary value problems. Indiana Univ. Math. J. 21, 125–146 (1971)

    Google Scholar 

  4. Anselone, P. M., & R. H. Moore, An extension of the Newton-Kantorovic method for solving nonlinear equations. J. Math. Anal. Appl. 13, 476–501 (1966)

    Google Scholar 

  5. Aris, R., On stability criteria of chemical reaction engineering. Chem. Engrg. Sci. 24, 149–169 (1969)

    Google Scholar 

  6. Busse, F., The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30, 625–649 (1967)

    Google Scholar 

  7. Courant, R., & D. Hilbert, Methods of Mathematical Physics, Vol. I and II. New York: Interscience 1953, 1962

    Google Scholar 

  8. Crandall, M. G., & P. H. Rabinowitz, Bifurcation from simple eigenvalues. J. Func. Analysis 8, 321–340 (1971)

    Google Scholar 

  9. Iudovich, V. I., Stability of convection flows. PMM 31, 294–303 (1967)

    Google Scholar 

  10. Joseph, D. D., On the stability of the Boussinesq equations. Arch. Rational Mech. Anal. 20, 59–71 (1965)

    Google Scholar 

  11. Kato, T., Perturbation Theory for Linear Operators. Berlin: Springer-Verlag 1966

    Google Scholar 

  12. Keller, H. B., & D. S. Cohen, Some positone problems suggested by nonlinear heat generation. J. Math. Mech. 16, 1361–1376 (1967)

    Google Scholar 

  13. Kirchgässner, K., & P. Sorger, Stability analysis of branching solutions of the Navier-Stokes Equations. Proc. 12th Int. Congr. Appl. Mech., Edited by M. Hetenyi and W. G. Vincenti. New York: Springer-Verlag

  14. Krein, M. G., & M. A. Rutman, Linear operators which leave a cone in Banach space invariant. Amer. Math. Soc. Transl. (1) 10, 199–325 (1950)

    Google Scholar 

  15. Krishnamurti, R., Finite amplitude convection with changing mean temperature, Part I. Theory. J. Fluid Mech. 33, 445–455 (1968)

    Google Scholar 

  16. Laetsch, T., The number of solutions of a nonlinear two point boundary value problem. Indiana Univ. Math. J. 20, 1–14 (1970)

    Google Scholar 

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

    Google Scholar 

  18. Rabinowitz, P. H., Some aspects of nonlinear eigenvalue problems. Rocky Mt. J. Math. 3, 161–202 (1973)

    Google Scholar 

  19. Sattinger, D. H., Stability of bifurcating solutions by Leray-Schauder degree. Arch. Rat. Mech. Anal. 43, 154–166 (1971)

    Google Scholar 

  20. Sattinger, D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems. Ind. U. Math. J. 21, 979–1000 (1973)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles

    Michael G. Crandall & Paul H. Rabinowitz

  2. Department of Mathematics, University of Wisconsin, Madison

    Michael G. Crandall & Paul H. Rabinowitz

Authors
  1. Michael G. Crandall
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  2. Paul H. Rabinowitz
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Additional information

Communicated by J. L. Lions

This research was sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462, by NSF Grant No. 144-C776, and by the Office of Naval Research Contracts N000-14-69-A-0200-4022 and N00014-67-A-0128-0024.

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Crandall, M.G., Rabinowitz, P.H. Bifurcation, perturbation of simple eigenvalues, itand linearized stability. Arch. Rational Mech. Anal. 52, 161–180 (1973). https://doi.org/10.1007/BF00282325

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  • DOI: https://doi.org/10.1007/BF00282325

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