Operator inclusions and quasi-variational inequalities
Vladimir Stepanovich Klimov · Mathematical Notes · 2017
The operator inclusion 0 ∈ A ( x ) + N ( x ) is studied. Themain results are concerned with the case where A is a bounded monotone-type operator from a reflexive space to its dual and N is a cone-valued operator. A criterion for this inclusion to have no solutions is obtained. Additive and homotopy-invariant integer characteristics of set-valued maps are introduced. Applications to the theory of quasi-variational inequalities with set-valued operators are given.