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Asymptotic stability of singularly perturbed linear system with unbounded delay. (English) Zbl 0622.34081

Differential equations: qualitative theory, 2nd Colloq., Szeged/Hung. 1984, Colloq. Math. Soc. János Bolyai 47, 1097-1124 (1987).
[For the entire collection see Zbl 0607.00010.]
A singulaly perturbed (with perturbation parameter \(\mu)\) linear differential system with unbounded delay is studied together with its associated degenerate \((\mu =0)\) system. The main result establishes, under certain smoothness conditions, equiasymptotic stability of the zero solution for \(\mu\) sufficiently small provided that the zero solution of the degenerate system is uniformly asymptotically stable, and that solutions of the perturbed system converge to solutions of the degenerate system as \(\mu\to 0\).
Reviewer: T.Gard

MSC:

34K20 Stability theory of functional-differential equations
34D15 Singular perturbations of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations

Citations:

Zbl 0607.00010