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Bulletin of the London Mathematical Society 2002 34(5):533-538; doi:10.1112/S002460930200108X
© 2002 by London Mathematical Society
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© London Mathematical Society

Bifurcation from Simple Eigenvalues and Eigenvalues of Geometric Multiplicity One

E. N. Dancer

School of Mathematics and Statistics, University of Sydney N.S.W. 2006, Australia normd{at}maths.usyd.edu.au

Received 11 December 2000. Revision received 1 June 2001.

A counterexample has been constructed to show that a conjectured global solution structure for bifurcation of non-trivial solutions from a simple eigenvalue of the linearization at zero really can occur. In addition, new results and counterexamples have been obtained for bifurcation from an eigenvalue of geometric multiplicity 1 and odd algebraic multiplicity. 2000 Mathematics Subject Classification 58E07, 47J15, 37G10.


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