On variational inequalities involving mappings of type (S)

Abstract

Variational inequalities can be converted into inclusions defined by a sum between a mapping of monotone type and a subdifferential. In our case, a topological approach of variational inequalities is based on a degree function for a (S)-operator F with maximal monotone perturbations T. The paper surveys some new advances on topological degree in the case F + T, removing the condition 0 ∈ T(0). In this way, the main difficulty is to determine the admissible homotopies. A graph homotopy for maximal monotone mappings is introduced. Finally, we mention some recent references regarding the related fixed point index.