Variational Inequalities and Analogs of the Hopf Theorems

V. S. Klimov

P.G. Demidov Yaroslavl State University

Abstract: Properties of the approximate rotation of vector fields generated by multivalued maps of monotone type are studied. Analogs of the Hopf theorems on the extension of multivalued maps without singular points and homotopy classification of the corresponding vector fields are proved. Applications to variational inequalities and operator inclusions are outlines.

Keywords: variational inequality, operator inclusion, relative degree, multivalued map, convex set.

UDC: 517.946

Received: 13.10.2018
Revised: 29.05.2019

DOI: 10.4213/mzm12222

 English version: Mathematical Notes, 2020, 108:1, 64–76

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