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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Markov stability
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Proc. Amer. Math. Soc. 72 (1978), 85-88 Request permission

Abstract:

The concept of T-stability for vector-valued functions is introduced—a generalization of strong stability in the sense of Markov. Moreover, for solutions of T-periodic systems of differential equations, T-stability is compared with Liapunov stability and it is shown that boundedness and T-stability imply asymptotic almost periodicity.
References
  • A. Markoff, Stabilität im Liapounoffschen Sinne und Fastperiodizität, Math. Z. 36 (1933), no. 1, 708–738 (German). MR 1545367, DOI 10.1007/BF01188645
  • A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
  • Maurice Fréchet, Les fonctions asymptotiquement presque-périodiques, Revue Sci. (Rev. Rose Illus.) 79 (1941), 341–354 (French). MR 13242
  • A. Halanay, Differential equations: Stability, oscillations, time lags, Academic Press, New York-London, 1966. MR 0216103
  • T. Yoshizawa, Stability theory and the existence of periodic solutions and almost periodic solutions, Applied Mathematical Sciences, Vol. 14, Springer-Verlag, New York-Heidelberg, 1975. MR 0466797
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 72 (1978), 85-88
  • MSC: Primary 34D99; Secondary 34C25
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0492632-8
  • MathSciNet review: 0492632