Abstract
The radius of stability and the radius of instability of the zero solution of the differential equation x’ = f (t, x) were introduced by Salvadori and Visentin [9], [10]. These radii in some sense provide a measure of the “region” of stability or instability of the zero solution. This knowledge has been used in the study of small solutions x p (t)of perturbations of the differential equation x’ = f (t, x) given by x’ = f(t, x p ) + h(t, x p ). In particular a relationship between the radius of stability of the zero solution of x’ = f (t, x) and its total stability was also introduced in [9] and [10]. Having been motivated by mechanical systems subject to conservative perturbations these authors analyzed the total stability of x’ = f (t, x) using the perturbed differential equation x’ = g (t, x, λ,) where g (t, x, 0) = f (t, x) and λ is a parameter in some Banach Space β. In this paper we often will assume β is the real line.
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© 2001 Kluwer Academic Publishers
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Anderson, P., Bernfeld, S.R. (2001). Properties of the Radii of Stability and Instability. In: Vajravelu, K. (eds) Differential Equations and Nonlinear Mechanics. Mathematics and Its Applications, vol 528. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0277-3_1
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DOI: https://doi.org/10.1007/978-1-4613-0277-3_1
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