Poincaré-Hopf type formulas on convex sets of Banach spaces
Keywords
Fixed point index on convex sets, Conley index on convex sets, Poincaré-Hopf formula, critical groupsAbstract
We consider locally Lipschitz and completely continuous maps $A\colon C\to C$ defined on a closed convex subset $C\subset X$ of a Banach space $X$. The main interest lies in the case when $C$ has empty interior. We establish Poincaré-Hopf type formulas relating fixed point index information about $A$ with homology Conley index information about the semiflow on $C$ induced by $-{\rm id}+A$. If $A$ is a gradient we also obtain results on the critical groups of isolated fixed points of $A$ in $C$.Downloads
Published
2009-12-01
How to Cite
1.
BARTSCH, Thomas and DANCER, E. Norman. Poincaré-Hopf type formulas on convex sets of Banach spaces. Topological Methods in Nonlinear Analysis. Online. 1 December 2009. Vol. 34, no. 2, pp. 213 - 229. [Accessed 24 April 2024].
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