@article{Bartsch_Dancer_2009, title={Poincaré-Hopf type formulas on convex sets of Banach spaces}, volume={34}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2009.039}, abstractNote={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 $C$.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Bartsch, Thomas and Dancer, E. Norman}, year={2009}, month={Dec.}, pages={213–229} }