Mixed semi-continuous perturbation of time -dependent maximal monotone operators and subdifferentials

We are concerned in the present work with the existence of absolutely continuous solutions to a class of evolution problems governed by time-dependent maximal monotone operators A(t) of the form − du dt (t) ∈ A(t)u(t) + f (t, u(t)) + F (t, u(t)), where the perturbation is a sum of a mixed semi-continuous compact set-valued map F and a singlevalued map f. New variants dealing with a class of time-dependant subdifferential operators of the form − du dt (t) ∈ ∂ϕ(t, u(t)) + f (t, u(t)) + F (t, u(t)) are also investigated. Some applications are given.