Abstract:
Using specific examples, it is proved that the presence of radial stability, asymptotic stability or complete instability (of any type: Lyapunov, Perron or upper-limit) properties of a non-one-dimensional autonomous nonlinear differential system, along each ray starting from zero, generally speaking, does not imply the presence of stability, asymptotic stability or, accordingly, complete instability of the same type.
Key words:differential system, nonlinear system, Lyapunov stability, Perron stability, upper-limit stability, radial stability, almost stability, asymptotic properties of solutions.
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