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Spectral flow and bifurcation for a class of strongly indefinite elliptic systems

Published online by Cambridge University Press:  28 December 2017

Nils Waterstraat*
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK ([email protected])

Extract

We consider bifurcation of solutions from a given trivial branch for a class of strongly indefinite elliptic systems via the spectral flow. Our main results establish bifurcation invariants that can be obtained from the coefficients of the systems without using explicit solutions of their linearizations at the given branch. Our constructions are based on a comparison principle for the spectral flow and a generalization of a bifurcation theorem due to Szulkin.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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