Topological characteristics of multi-valued maps and Lipschitzian functionals
Vladimir Stepanovich Klimov · Izvestiya Mathematics · 2008
This paper deals with the operator inclusion , where is a multi-valued map of monotonic type from a reflexive space to its conjugate and is the cone normal to the closed set , 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 Poincare-Hopf theorem.