A K-theoretical invariant and bifurcation for a parameterized family of functionals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:377

Article

Portaluri, Alessandro

关键词: Abstract bifurcation theory;    Bifurcation theory;   

DOI  :  10.1016/j.jmaa.2010.11.009

来源: Elsevier

【 摘 要 】

Let F := {f(x): x epsilon X} be a family of functionals defined on a Hilbert manifold (E) over tilde and smoothly parameterized by a compact connected orientable n-dimensional manifold X, and let sigma : X -> (E) over tilde be a smooth section of critical points of F. The aim of this paper is to give a sufficient topological condition on the parameter space X which detects bifurcation of critical points for F from the trivial branch. Finally we are able to give some quantitative properties of the bifurcation set for perturbed geodesics on semi-Riemannian manifolds. (c) 2010 Elsevier Inc. All rights reserved.

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