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Bifurcation at eigenvalues of odd multiplicity

Author: David Westreich
Journal: Proc. Amer. Math. Soc. 41 (1973), 609-614
MSC: Primary 47H15
MathSciNet review: 0328707
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Abstract: The most general form of the bifurcation problem is considered. Under reasonable hypotheses, ``eigenvalues'' of odd multiplicity are shown to be bifurcation points.

References [Enhancements On Off] (What's this?)

  • [1] M. S. Berger and M. S. Berger, Perspectives in nonlinearity. An introduction to nonlinear analysis, Benjamin, New York, 1968. MR 40 #4971. MR 0251744 (40:4971)
  • [2] M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Analysis 8 (1971), 321-340. MR 44 #5836. MR 0288640 (44:5836)
  • [3] J. Dieudonné, Foundations of modern analysis, Pure and Appl. Math., vol. 10, Academic Press, New York, 1960. MR 22 #11074. MR 0120319 (22:11074)
  • [4] S. Goldberg, Unbounded linear operators. Theory and applications, McGraw-Hill, New York, 1966. MR 34 #580. MR 0200692 (34:580)
  • [5] M. M. Vainberg, Variational methods for the study of nonlinear operators, GITTL, Moscow, 1956; English transl., Holden-Day, San Francisco, Calif., 1964. MR 19, 567; 31 #638. MR 0176364 (31:638)
  • [6] D. Westreich, Banach space bifurcation theory, Trans. Amer. Math. Soc. 171 (1972), 135-156. MR 0328706 (48:7048)

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Keywords: Bifurcation, eigenvalues, odd multiplicity, Banach space, Fréchet differentiable, Fredholm operator, index zero, implicit function theorem, contraction map, continuous curve
Article copyright: © Copyright 1973 American Mathematical Society

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