Bifurcation with a two-dimensional kernel |
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Authors: | Stefan Krömer Hansjörg Kielhöfer |
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Institution: | a Institut für Mathematik, Universität Augsburg, Universitätsstrasse 14, 86135 Augsburg, Germany b Department of Theoretical and Applied Mechanics, Kimball Hall, Cornell University, Ithaca, NY 14853, USA |
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Abstract: | We present a theorem ensuring the existence of local solution branches for one-parameter bifurcation problems in which the linearization at the trivial solution possesses a two-dimensional kernel. In particular, we provide a straightforward “test” that is sufficient for the existence of local solution continua. We demonstrate our abstract theorem with several concrete examples for second-order systems of elliptic partial differential equations with symmetry. |
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Keywords: | Bifurcation Elliptic systems Symmetry methods |
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