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arXiv · 1210.0417

Bifurcation results for critical points of families of functionals

Alessandro Portaluri·Nils Waterstraat
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Abstract

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

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Alessandro Portaluri, Nils Waterstraat. 2012-09-28. Bifurcation results for critical points of families of functionals. https://arxiv.org/abs/1210.0417

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