Tikhonov's theorem for functional differential inclusions

Abstract

We investigate differential inclusions and equations of a retarded type with a small real parameter $\varepsilon > 0$ in part of the derivatives. Analogues of the well-known in the theory of singularly perturbed ordinary differential equations theorem of Tikhonov are obtained. We prove lower semicontinuity of the solution set for inclusions and continuity of the solution for equations in the most appropriate topology when $\varepsilon \rightarrow 0$.