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On a problem of Hahn

Published online by Cambridge University Press:  17 April 2009

W.A. Coppel
W.A. Coppel
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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It is shown that for any almost periodic linear differential system asymptotic stability and uniform stability together imply uniform asymptotic stability.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 14 , Issue 3 , June 1976 , pp. 321 - 324
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Conley, C.C. and Miller, R.K., “Asymptotic stability without uniform stability: almost periodic coefficients”, J. Differential Equations 1 (1965), 333–336.CrossRefGoogle Scholar
[2]Coppel, W.A., Stability and asymptotic behavior of differential equations (Heath, Boston, 1965).Google Scholar
[3]Hahn, Wolfgang, “The present state of Lyapunov's direct method”, Nonlinear problems, 195–205 (Proceedings of a Symposium conducted by the Mathematics Research Center, United States Army, University of Wisconsin, Madison, 1962. University of Wisconsin Press, Madison, 1963).Google Scholar
[4]Nakajima, Fumio, “Separation conditions and stability properties in almost periodic systems”, Ta¸hoku. Math. J. 26 (1974), 305–314.Google Scholar
[5]Sacker, Robert J. and Sell, George R., “Existence of dichotomies and invariant splittings for linear differential systems I”, J. Differential Equations 15 (1974), 429–458.CrossRefGoogle Scholar