Conley index in Hilbert spaces versus the generalized topological degree. (English) Zbl 1386.34068

Summary: We prove a version of the Poincaré-Hopf theorem suitable for strongly indefinite functionals and then apply it to infer a number of bifurcation results in infinite-dimensional Hilbert spaces.


34C23 Bifurcation theory for ordinary differential equations
47J15 Abstract bifurcation theory involving nonlinear operators
Full Text: Euclid