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- W2023142913 abstract "The stability of a system described by Volterra integrodifferential equations is investigated in the critical case when the characteristic equation has a pair of pure imaginery roots. Conditions for instability, analogous to the well-known conditions from the theory of differential equations [1], are derived. (A similar result was established previously in [2] for integrodifferential equations of simpler structure with integral kernels of exponential-polynomial type). For the proof, several manipulations are used to simplify the original equation and, in particular, to reduce the linearized equation to the form of a differential equation with constant diagonal matrix. (An analogous approach was used to analyse instability for Volterra integrodifferential equations in the critical case of zero root in [3, 4]). As an example, the sign of the Lyapunov constant in the problem of the rotational motion of a rigid body with viscoelastic supports is calculated." @default.
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- W2023142913 date "1998-01-01" @default.
- W2023142913 modified "2023-09-25" @default.
- W2023142913 title "Instability in the critical case of pair of pure imaginary roots for a class of systems with aftereffect" @default.
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- W2023142913 doi "https://doi.org/10.1016/s0021-8928(98)00008-2" @default.
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