Truncated Perturbation to Evolution Problems Involving Time-Dependent Maximal Monotone Operators

This paper is devoted to the study of an evolution inclusion with unbounded nonconvex valued perturbation that is driven by a time-dependent maximal monotone operator. As well the examination of the inclusion when the perturbation term is convexified. We establish the existence of solutions and the relaxation property between these evolution inclusions via the truncated Lipschitz property.