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Global Stability Determined by Local Properties and the First Variation

Published online by Cambridge University Press:  20 November 2018

R. Datko
R. Datko*
Affiliation:
McGill University
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In this note we consider a system of autonomous differential equations

1.1

where f: En → En is a continuously differentials Le mapping for n ≥ 2. We shall assume that f(0) = 0 and that the origin is locally asymptotically stable.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 1 , April 1966 , pp. 89 - 94
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Hartman, P. and Olech, C., On global asymptotic stability of solutions of differential equations, Trans. Amer. Math. Soc vol. 104 (1962) pp. 154-178.Google Scholar
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3. Markus, L. and Yamabe, H., Global stability criterion for differential systems, Osaka Math. Jour., vol. 12 (1960) pp. 305-317.Google Scholar
4. Hartman, P., Stability in the large, Canadian Jour, of Math. vol. 13 (1961) pp. 480-492.Google Scholar