Nonlinear second order differential inclusions with a series of convex functions

In this paper, we study a class of second order differential inclusions attached to which the convex potential varies depending on the time, and the boundary conditions are described by the subdifferentials of convex functions. Applying the theory of lower semicontinuous, convex and proper functionals, and fixed points, we give some results about the representation of the subdifferential operators of some convex functionals and the existence of solutions for the boundary value problems.