On singular perturbations for differential inclusions on the infinite interval

Abstract 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 , + ∞ [ .

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