  In this paper, we first investigate an abstract subdifferential for which
(using Ekeland's variational principle) we can prove an analog of the
Br{\o}ndsted-Rockafellar property. We introduce the "$r_L$-density" of a subset
of the product of a Banach space with its dual. A closed $r_L$-dense monotone
set is maximally monotone, but we will also consider the case of nonmonotone
closed $r_L$-dense sets. As a special case of our results, we can prove
Rockafellar's result that the subdifferential of a proper convex lower
semicontinuous function is maximally monotone.
