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References (16)
-
On studying Perron stability of one - dimensional and autonomous differential systems -
(2019)
On studying Perron and Lyapunov properties by the first approximation, Differ -
I. Sergeev (2019)
Dependence and Independence of the Perron and Lyapunov Stability Properties on the System Phase DomainDifferential Equations, 55
-
(2019)
Lyapunov and Perron stability of solutions of differential systems, in Sovr -
(2019)
One example of unstable system, Differ -
(2018)
Definition of Perron stability and its relationship with Lyapunov stability, Differ -
(2019)
On Perron and Lyapunov stability of solutions, in XIX Mezhdunar -
(1966)
Teoriya pokazatelei Lyapunova i ee prilozheniya k voprosam ustoichivosti (Theory of Lyapunov Exponents and Its Applications to Problems of Stability) -
I. Sergeev (2019)
Definition and Some Properties of Perron StabilityDifferential Equations, 55
-
O. Perron (1930)
Die Ordnungszahlen linearer DifferentialgleichungssystemeMathematische Zeitschrift, 31
-
Ustoichivost' i kolebaniya nelineinykh sistem upravleniya" (konferentsiya Pyatnitskogo). 30 maya-1 iyunya 2018 g -
(2019)
Perron and Lyapunov stability properties and their investigation by the first approximation, in Mater. III mezhdunar. nauch. konf -
(2006)
Vvedenie v teoriyu pokazatelei Lyapunova (Introduction to the Theory of Lyapunov Exponents), Minsk: Belarus -
(1950)
Obshchaya zadacha ob ustoichivosti dvizheniya (General Problem of Motion Stability) -
I. Sergeev (2019)
Perron Stability and Its Study at the First ApproximationDoklady Mathematics, 99
-
(2018)
Perron stability and simplified central Vinograd–Millionshchikov exponents, in Tez. dokl. XIV mezhdunar. konf. “Ustoichivost’ i kolebaniya nelineinykh sistem upravleniya
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2020
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266120010097
- Publisher site
- See Article on Publisher Site
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.
Journal
Differential Equations – Springer Journals
Published: Jan 25, 2020