On singular perturbations for differential inclusions on the infinite interval

We consider a differential inclusion subject to a singular perturbation, i.e., part of the derivatives are multiplied by a small parameter ɛ>0. We show that under some stability and structural assumptions, every solution of the singularly perturbed inclusion comes close to a solution of the degenerate inclusion (obtained for ɛ=0) when ɛ tends to 0. The goal of the present paper is to provide a new result of Tikhonov type on the time interval [0,+∞[.