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March/April 2014 Bifurcation results for critical points of families of functionals
Alessandro Portaluri, Nils Waterstraat
Differential Integral Equations 27(3/4): 369-386 (March/April 2014).

Abstract

Recently, the first author studied in [17] the bifurcation of critical points of families of functionals on a Hilbert space, which are parametrized 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 generalize it to a broader class of functionals. From the topological point of view, we allow the parameter space to be a metrizable 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.

Citation

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Alessandro Portaluri. Nils Waterstraat. "Bifurcation results for critical points of families of functionals." Differential Integral Equations 27 (3/4) 369 - 386, March/April 2014.

Information

Published: March/April 2014
First available in Project Euclid: 30 January 2014

zbMATH: 1324.47108
MathSciNet: MR3161608

Subjects:
Primary: 58E07, 58E10

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 3/4 • March/April 2014
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