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

Part of: Elliptic equations and systems Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  28 December 2017

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

Keywords

variational bifurcation theoryspectral flowelliptic systems

MSC classification

Primary: 35J57: Boundary value problems for second-order elliptic systems
Secondary: 58J30: Spectral flows 35J61: Semilinear elliptic equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 5 , October 2018 , pp. 1097 - 1113
Copyright
Copyright © Royal Society of Edinburgh 2018 

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