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We develop a degree theory for variational inequalities which contain multivalued (S$_+$)-perturbations of maximal monotone operators. The multivalued operators need not necessarily be convex-valued. The result is simultaneously an extension of a degree theory for variational inequalities (developed by Benedetti, Obukhovskii and Zecca) and of the Skrypnik-Browder degree and extensions thereof.

A degree theory for variational inequalities with sums of maximal monotone and (S$_+$) operators