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Operator inclusions and quasi-variational inequalities

  • Volume 101, Number 5, May, 2017
  • Published:
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Abstract

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.

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Authors and Affiliations

  1. Demidov Yaroslavl State University, Yaroslavl, Russia

    V. S. Klimov

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  1. V. S. Klimov
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Correspondence to V. S. Klimov.

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Original Russian Text © V. S. Klimov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 5, pp. 750–767.

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Klimov, V.S. Operator inclusions and quasi-variational inequalities. Math Notes 101, 863–877 (2017). https://doi.org/10.1134/S0001434617050121

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