A result on the singular perturbation theory for differential inclusions in Banach spaces

Abstract

We provide conditions which ensure that the solution set of the Cauchy problem for a singularly perturbed system of differential inclusions in infinite dimensional Banach spaces is upper semicontinuous with respect to the parameter $\varepsilon\ge0$ of the perturbation. The main tools are represented by suitable introduced measures of noncompactness and the topological degree theory in locally convex spaces.