Differential and Integral Equations

Bifurcation results for critical points of families of functionals

Alessandro Portaluri and Nils Waterstraat

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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.

Article information

Differential Integral Equations, Volume 27, Number 3/4 (2014), 369-386.

First available in Project Euclid: 30 January 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 58E07: Abstract bifurcation theory 58E10: Applications to the theory of geodesics (problems in one independent variable)


Portaluri, Alessandro; Waterstraat, Nils. Bifurcation results for critical points of families of functionals. Differential Integral Equations 27 (2014), no. 3/4, 369--386. https://projecteuclid.org/euclid.die/1391091370

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