Igor N. Sergeev
abstract:
The natural concepts of Lyapunov, Perron and upper-limit stability of the zero
solution of a differential system are defined, as well as their numerous
varieties: from global to particular stability or, respectively, instability. A
complete coincidence of possibilities of research on the first approximation of
stability and asymptotic stability of all three types is found. A similar
coincidence was established for partial and particular stability. The complete
coincidence of the same possibilities in the case of one-dimensional systems is
proved.
Mathematics Subject Classification: 34D05, 34D20, 34D23
Key words and phrases: Differential system, Lyapunov stability, Lyapunov and Perron exponents, first approximation stability, Perron stability, upper-limit stability