A global bifurcation theorem for critical values in Banach spaces (Q2420253)

The authors prove three bifurcation results. The first one shows the existence of a global bifurcation branch of critical values of a $C^1$-map $f:\mathbb{R} \times X \to \mathbb{R}$, where $X$ is a real Banach space, and $f$ satisfies (PS)-type and appropriate topological conditions (homotopy type of pairs of sublevel sets differ). \par The second one is in separable Hilbert space, $f$ is $C^2$ , Morse indices of the Hessian are finite and they change ( plus other technical conditions). \par In the strongly indefinite case the authors use the spectral flow to obtain the conclusion.