Studying the Perron and Lyapunov stability properties by the first approximation (Q2188055)

The present paper deals with developing and investigating the classical notion of Lyapunov stability, as well as the recently introduced counterpart of this notion, Perron stability, going back to Perron exponents. These properties, as well as their diverse modifications, including the opposites, are studied in this paper primarily from the viewpoint of the possibility of examining them by the first approximation.