Singularly perturbed functional-differential inclusions

Differential inclusions of a retarded type with a small real parameter ε>0 in part of the derivatives are considered. We prove upper semicontinuity of the map ‘ε → set of solutions’ at ε=0+ inC[0, 1]×(L2(0, 1)−weak) topology. In case of constant delay lower semicontinuity inC[0, 1]×(L1(0, 1)−strong) is shown.