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

TL;DR

This paper investigates bifurcation phenomena in strongly indefinite elliptic systems using spectral flow, introducing invariants that do not require explicit linearization solutions, thus advancing bifurcation analysis methods.

Contribution

It develops new bifurcation invariants derived from system coefficients, extending spectral flow techniques without relying on explicit linearization solutions.

Findings

Established bifurcation invariants from coefficients

Generalized Szulkin's bifurcation theorem

Provided a comparison principle for spectral flow

Abstract

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.