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On the Relationship Between the Optimal Derivative and Asymptotic Stability

Volume 8, Number 2 (2009), 148 - 162

On the Relationship Between the Optimal Derivative and Asymptotic Stability

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Abstract

The aim of this paper is to present the relationship between the optimal derivative and asymptotic stability of a nonlinear ordinary equation. We provide an example where the study of stability of the equilibrium point is a problem; the linearization of the differential equations at the origin has purely imaginary eigenvalues and thus the stability type of the equilibrium point at the origin cannot be deduced from the linear approximation.