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

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 way to apply a comparison principle which is based on an index theorem for a certain class of Fredho...

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Bibliographic Details
Published in:Nonlinear differential equations and applications Vol. 32; no. 6; p. 116
Main Authors: Janczewska, Joanna, Möckel, Melanie, Waterstraat, Nils
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01.11.2025
Subjects:
Bifurcations
Eigenvalues
Elliptic differential equations
Hilbert space
Parabolic differential equations
Partial differential equations
Theorems
ISSN:1021-9722, 1420-9004
Online Access:Get full text
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Summary: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 way to apply a comparison principle 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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ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-025-01126-7