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Recently the first author studied the bifurcation of critical points offamilies of functionals on a Hilbert space, which are parametrised by a compactand orientable manifold having a non-vanishing first integral cohomology group.We improve this result in two directions: topologically and analytically. Fromthe analytical point of view we generalise it to a broader class offunctionals; from the topological point of view we allow the parameter space tobe a metrisable Banach manifold. Our methods are in particular powerful if theparameter space is simply connected. As an application of our results weconsider families of geodesics in (semi-) Riemannian manifolds.

Bifurcation results for critical points of families of functionals