  We study an abstract second order inclusion involving two nonlinear
single-valued operators and a nonlinear multivalued term. Our goal is to
establish the existence of solutions to the problem by applying numerical
scheme based on time discretization. We show that the sequence of approximate
solution converges weakly to a solution of the exact problem. We apply our
abstract result to a dynamic, second order in time differential inclusion
involving Clarke subdifferential of a locally Lipschitz, possibly nonconvex and
nonsmooth potential. In two presented examples the Clarke subdifferential
appears either in a source term or in a boundary term.
