We study the relationship between the Mosco convergence of a sequence of convex proper lower semicontinuous functionals, defined on a reflexive Banach space, and the convergence of their subdifferentiels as maximal monotone graphs. We then apply these results together with the unfolding method (see \cite{CioranescuDamlamianGriso2002}) to study the homogenization of equations of the form $-\textrm{ div }d_\varepsilon=f $, with $(\nabla u_\varepsilon(x),d_\varepsilon(x)) \in \partial \varphi_\varepsilon(x)$ where $\varphi_\varepsilon (x,.)$ is a Carathéodory convex function with suitable growth and coercivity conditions.