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

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 linearisations at the given branch. Our constructions are based on a comparison principle for the spectral flow and a generalisation of a bifurcation theorem due to Szulkin.