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arXiv · 2405.19473

Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem

J. Janczewska·M. Möckel·N. Waterstraat
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Abstract

We consider families of strongly indefinite systems of elliptic PDE and investigate bifurcation from a trivial branch of solutions by using the spectral flow. The novelty in our approach is a refined version of a comparison principle that was originally proved by Pejsachowicz in a joint work with the third author, and which is based on an index theorem for a certain class of Fredholm operators that is of independent interest. Finally, we use our findings for a bifurcation problem on shrinking domains that originates from works of Morse and Smale.

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J. Janczewska, M. Möckel, N. Waterstraat. 2024-05-29. Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem. https://arxiv.org/abs/2405.19473

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