On limiting transition in a singular perturbed system of functional-differential equations (Q2759342)
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scientific article; zbMATH DE number 1681760
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On limiting transition in a singular perturbed system of functional-differential equations |
scientific article; zbMATH DE number 1681760 |
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12 December 2001
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functional-differential equations
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singular perturbation
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asymptotic stability
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delay
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On limiting transition in a singular perturbed system of functional-differential equations (English)
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The author considers a singular perturbed system of weak delay functional-differential equations. For this system the asymptotic behaviour of solutions is investigated. Sufficient conditions that guarantee the convergence of the solutions to the corresponding solutions of a limiting system are presented in the case when the main condition of the classical Tikhonov theorem on the limiting transition in singular perturbed systems (the condition of uniform asymptotic stability of a rest point of an adjoined system) is replaced by the weaker condition of nonasymptotic Lyapunov stability.
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