Let be an open subset of a real Hilbert space H, whose norm and scalar product are denoted by and (. If is a function, set
If f is lower semicontinuous (with respect to the norm topology), f is said to have a -monotone subdifferential, if there exists a continuous function such that
whenever , , , . In this paper some general properties of this class of functions are studied and some theorems of existence, uniqueness, regularity and convergence, concerning the associated evolution equation are proved.