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

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Main Authors: Janczewska, J., Möckel, M., Waterstraat, N.
Format: Preprint
Published: 2024
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author Janczewska, J.
Möckel, M.
Waterstraat, N.
author_facet Janczewska, J.
Möckel, M.
Waterstraat, N.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2405_19473
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem
Janczewska, J.
Möckel, M.
Waterstraat, N.
Analysis of PDEs
Functional Analysis
Spectral Theory
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.
title Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem
topic Analysis of PDEs
Functional Analysis
Spectral Theory
url https://arxiv.org/abs/2405.19473