  In this paper we study nonlinear second-order differential inclusions
involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone
operator and nonlinear multivalued boundary conditions. Our framework is
general and unifying and incorporates gradient systems, evolutionary
variational inequalities and the classical boundary value problems, namely the
Dirichlet, the Neumann and the periodic problems. Using notions and techniques
from the nonlinear operator theory and from multivalued analysis, we obtain
solutions for both the `convex' and `nonconvex' problems. Finally, we present
the cases of special interest, which fit into our framework, illustrating the
generality of our results.
