Abstract

Various Perron stability properties of a two-dimensional differential system are studied. It is proved that, generally speaking, the complete Perron instability does not imply the global Perron instability, which may seem at first glance. It turns out that it is possible to construct a counterexample even with an infinitely differentiable right-hand side and a zero matrix of the first approximation at zero. The system under consideration is nonlinear.

中文翻译：

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一个完整但非全局 Perron 不稳定性的例子

摘要

研究了二维微分系统的各种 Perron 稳定性特性。事实证明，一般来说，完全 Perron 不稳定性并不意味着全局 Perron 不稳定性，这乍一看似乎是。事实证明，即使具有无限可微的右手边和一阶近似为零的零矩阵，也可以构造一个反例。所考虑的系统是非线性的。