### Abstract inclusions in Banach spaces with boundary conditions of periodic type

We study in the space of continuous functions defined on [0,T] with values in a real Banach space E the periodic boundary value problem for abstract inclusions of the form ⎧ $x\in S(x\left(0\right),se{l}_{F}\left(x\right))$ ⎨ ⎩ x (T) = x(0), where, $F:[0,T]\times \to {2}^{E}$ is a multivalued map with convex compact values, ⊂ E, $se{l}_{F}$ is the superposition operator generated by F, and S: × L¹([0,T];E) → C([0,T]; ) an abstract operator. As an application, some results are given to the periodic boundary value problem for nonlinear differential inclusions governed by m-accretive...