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

Nils Waterstraat

doi:10.1017/S0308210517000324

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

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

Published online by Cambridge University Press: 28 December 2017

Nils Waterstraat

Show author details

Nils Waterstraat*: Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, Kent CT2 7NF, UK (n.waterstraat@kent.ac.uk)

Article contents

Extract

Rights & Permissions

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.