On Stability in the Large for Systems of Ordinary Differential Equations
- 1 January 1961
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 13, 480-492
- https://doi.org/10.4153/cjm-1961-040-6
Abstract
Autonomous systems. This note concerns the stability of systems of (real) differential equations in the large on Euclidean space En and on certain Riemannian manifolds Mn. The results will be refinements of those of Krasovski (3), (4), (5) and of Markus and Yamabe (8) and will make clear the role of the various assumptions in the type of theorems under consideration.In this section, the main theorems are stated for autonomous systems (1) Their proofs are given in § 2, 3, 4. In § 5, 6, 7, generalizations to non-autonomous systems are made.Keywords
This publication has 5 references indexed in Scilit:
- Sur la stabilité asymptotique des solutions d'un système d'équations différentiellesAnnales Polonici Mathematici, 1959
- Theorie und Anwendung der direkten Methode von LjapunovPublished by Springer Nature ,1959
- Differential Equations Referred to a Variable MetricAmerican Journal of Mathematics, 1951
- Asymptotic Integration ConstantsAmerican Journal of Mathematics, 1946
- Remarks on Systems of Ordinary Differential EquationsAmerican Journal of Mathematics, 1937