We are interested in constructing a topological degree for operators of the
form F=L+A+S, where L is a linear densely defined maximal
monotone map, A is a bounded maximal monotone operators, and S is a bounded demicontinuous map of class (S+) with respect to
the domain of L. By means of this topological degree we prove an
existence result that will be applied to give a new formulation of
a parabolic variational inequality problem.