Topological degree for (S)image-mappings with maximal monotone perturbations and its applications to variational inequalities Original Research Article

This paper is concerned with the topological degree for mappings of class (S)++ with maximal monotone perturbations. Several results and remarks concerning the evaluation of this degree are given. In particular, it is shown that the local degree for the generalized gradient of nonsmooth functional at the local minimizer is equal to one. As applications, two examples of elliptic variational inequalities are given, where the multiple existence of solutions is discussed.