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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.

MSC:

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