Abstract
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 $C$.
Citation
Thomas Bartsch. Norman Dancer. "Poincaré-Hopf type formulas on convex sets of Banach spaces." Topol. Methods Nonlinear Anal. 34 (2) 213 - 229, 2009.
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