Geodesic
Topological characteristics of multi-valued maps and Lipschitzian functionals
Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 717-739

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This paper deals with the operator inclusion $0\in F(x)+N_Q(x)$, where $F$ is a multi-valued map of monotonic type from a reflexive space $V$ to its conjugate $V^*$ and $N_Q$ is the cone normal to the closed set $Q$, which, generally speaking, is not convex. To estimate the number of solutions of this inclusion we introduce topological characteristics of multi-valued maps and Lipschitzian functionals that have the properties of additivity and homotopy invariance. We prove some infinite-dimensional versions of the Poincaré–Hopf theorem. 
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     author = {V. S. Klimov},
     title = {Topological characteristics of multi-valued maps and {Lipschitzian} functionals},
     journal = {Izvestiya. Mathematics },
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     year = {2008},
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     url = {http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a4/}
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V. S. Klimov. Topological characteristics of multi-valued maps and Lipschitzian functionals. Izvestiya. Mathematics , Tome 72 (2008) no. 4, pp. 717-739. http://geodesic.mathdoc.fr/item/IM2_2008_72_4_a4/