Abstract
The author considers systems of differential equations with after-effect that contain a small parameter as a coefficient of the derivatives. On the basis of the given uniform asymptotic stability of the degenerate system of differential equations, and of the uniform stepwise asymptotic stability of a certain auxiliary system, he establishes the uniform asymptotic stability of the original system. The problem are treated by the Liapunov-Chetaev [ 1,2 ] method developed for systems of equations with the after-effect by Krasovskii [ 3 ]. It is mentioned that problem on the stability of systems of differential equations with after-effect containing a small parameter were considered by El'sgol'ts [ 4 ]. The present work extends certain results of Krasovskii [ 5 ] to systems with after-effect.
Published Version
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