Bifurcation for a Class of Indefinite Elliptic Systems by Comparison Theory for the Spectral Flow via an Index Theorem

2024/05/29 by Janczewska, J., Möckel, M., Waterstraat, N.
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2405.19473

Abstract

We consider families of strongly indefinite systems of elliptic PDE and investigate bifurcation from a trivial branch of solutions by using the spectral flow. The novelty in our approach is a refined version of a comparison principle that was originally proved by Pejsachowicz in a joint work with the third author, and which is based on an index theorem for a certain class of Fredholm operators that is of independent interest. Finally, we use our findings for a bifurcation problem on shrinking domains that originates from works of Morse and Smale.

Related

• Spectral flow and bifurcation for a class of strongly indefinite elliptic systems
• Global bifurcation index of critical orbit of strongly indefinite functional
• The Equivariant Spectral Flow and Bifurcation for Functionals with Symmetries -- Part I
• On a Comparison Principle and the Uniqueness of Spectral Flow
• Unilateral global bifurcation for a class of quasilinear elliptic systems and applications