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

Alessandra Andreini, Mikhail I. Kamenskiń≠, Paolo Nistri

DOI: http://dx.doi.org/10.12775/TMNA.2000.001

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.

Keywords


Singularly perturbed systems; differential inclusions; condensing operators; locally convex spaces

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