An averaging method for singularly perturbed system of semilinear differential inclusions with C_0 semigroup

We consider a system of two semilinear differential inclusions with infinitesimal generators of C0-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x, y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for ε > 0 sufficiently small, the existence of periodic solutions and to study their behaviour as ε → 0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.