Studying the Perron and Lyapunov Stability Properties by the First Approximation
Igor Nikolaevich Sergeev · Differential Equations · 2020
Abstract We explore opportunities for studying various Perron or Lyapunov stability properties of differential systems by the first approximation. We prove that the linear approximations guaranteeing at least one of the four properties (stability or asymptotic stability in the sense of Perron or Lyapunov) also ensure the remaining three properties, i.e., that all four respective classes of linear approximations coincide. The classes of linear approximations guaranteeing partial Lyapunov or Perron stability coincide as well, and all six above-listed classes coincide in the one-dimensional case.