Classes of Linear Approximations Providing Different Stability or Instability Types of Differential Systems.

The paper studies relationships (inclusions, coincidences, and noncoincidences) between classes of linear approximations that provide various properties of Lyapunov, Perron, and upper-limit stability or instability (from global to particular) of the zero solution to a differential system of arbitrary order. A complete set of noncoinciding stability classes is presented and some considerations are given for a similar description of instability classes. [ABSTRACT FROM AUTHOR]