Bifurcation results for critical points of families of functionals

Portaluri, Alessandro and Waterstraat, Nils (2014) Bifurcation results for critical points of families of functionals. Differential Integral Equations, 27 . pp. 369-386. ISSN 0893-4983. (Full text available)

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.

Item Type: Article
Additional information: Imported from arXiv
Subjects: Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Nils Waterstraat
Date Deposited: 03 Nov 2015 16:06 UTC
Last Modified: 07 Feb 2017 22:53 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/51395 (The current URI for this page, for reference purposes)
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