Differential Equations

, Volume 55, Issue 5, pp 620–630 | Cite as

Definition and Some Properties of Perron Stability

  • I. N. SergeevEmail author
Ordinary Differential Equations


The natural notions of Perron stability, Perron asymptotic stability, and Perron complete instability of the zero solution of a differential system are introduced. Peculiar features of these notions are noted in the one-dimensional, autonomous, and linear cases. Their connections with Perron exponents and with their counterparts in the sense of Lyapunov are described. The complete coincidence of the possibilities for studying the Perron and Lyapunov stability and asymptotic stability in the first approximation is revealed.


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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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