On problems involving second order differential inclusions in Banach spaces.

This thesis provides a contribution to the study of second order differential inclusions in abstract spaces, examining different types of problem. The proofs of the existence results are based on a combination of a fixed point methods with selection theorems and, where useful, on the utilization of the measure of weak noncompactness. The mentioned approach has the advantage of not requiring compactness assumptions on the operators and multivalued terms that characterize the differential inclusions studied. This is particularly important because in infinite-dimensional spaces, compactness assumptions are often not satisfied. Another contribution is, in the last two chapters, the study of optimal control through a coercive and lower semicontinuous operator for a problem involving second order ordinary/partial differential equations.