On boundary value problems in Banach spaces

The paper deals with boundary value problemsassociated to first-order differential inclusions in Banach spaces. The solvability is investigated in the (strong) Carathèodory sense on compact intervals. To this aim, we develop a general method that relies on degree arguments. This method is still combined with a bound sets technique for checking the behavior of trajectories in the neighborhood of a suitable parametric set of candidate solutions. On this basis, we obtain effective criteria for the existence of solutions of Floquet problems. The existence of entirely bounded solutions is also established by means of a sequence of solutions on compact increasing intervals.