This article is cited in 1 paper

Operator Inclusions and Quasi-Variational Inequalities

V. S. Klimov

P.G. Demidov Yaroslavl State University

Abstract: The operator inclusion $0\in A(x)+N(x)$ is studied. The main 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.

Keywords: operator inclusion, multimap, quasi-variational inequality, vector field, convex set.

UDC: 517.946

Received: 29.11.2015
Revised: 05.04.2016

DOI: 10.4213/mzm11022

 English version: Mathematical Notes, 2017, 101:5, 863–877

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