Topological Methods in Nonlinear Analysis

Poincaré-Hopf type formulas on convex sets of Banach spaces

Thomas Bartsch and Norman Dancer

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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 $C$.

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Topol. Methods Nonlinear Anal., Volume 34, Number 2 (2009), 213-229.

First available in Project Euclid: 27 April 2016

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Bartsch, Thomas; Dancer, Norman. Poincaré-Hopf type formulas on convex sets of Banach spaces. Topol. Methods Nonlinear Anal. 34 (2009), no. 2, 213--229.

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