Geodesic
Operator Inclusions and Quasi-Variational Inequalities
Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 750-767

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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, quasi-variational inequality, vector field, convex set.
Mots-clés : multimap 
@article{MZM_2017_101_5_a9,
     author = {V. S. Klimov},
     title = {Operator {Inclusions} and {Quasi-Variational} {Inequalities}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {750--767},
     publisher = {mathdoc},
     volume = {101},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a9/}
}
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V. S. Klimov. Operator Inclusions and Quasi-Variational Inequalities. Matematičeskie zametki, Tome 101 (2017) no. 5, pp. 750-767. http://geodesic.mathdoc.fr/item/MZM_2017_101_5_a9/