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Frequency entrainment for almost periodic evolution equations


Author: James Murdock
Journal: Proc. Amer. Math. Soc. 96 (1986), 626-628
MSC: Primary 34C27; Secondary 35B15
DOI: https://doi.org/10.1090/S0002-9939-1986-0826492-4
MathSciNet review: 826492
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Abstract: A theorem of Massera stating that periodic solutions of equations are (under a simple hypothesis) entrained is generalized to limit periodic equations and (with a weak definition of entrainment) to almost periodic equations. An error is explained in a stronger result claimed by Cartwright.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch, Almost periodic functions, Dover, New York, 1954. MR 0068029 (16:817a)
  • [2] M. L. Cartwright, Almost periodic differential equations and almost periodic flows, J. Differential Equations 5 (1969), 167-181. MR 0239191 (39:548)
  • [3] N. Forbat, Amalytische Mechanik der Schwingungen, V.E.B. Deutsche Verlag der Wissenschaft, Berlin, 1966.
  • [4] P. Hagedorn, Non-linear oscillations, translated by W. Stadler, Clarendon Press, Oxford, 1981.
  • [5] J. Massera, Observaciones sobre las soluciones periodicas de ecuaciones diferenciales, Bol. Fac. Ingen. Montevideo 4 (1950-53), 37-45. MR 0047866 (13:944e)
  • [6] G. O'Brien, The frequencies of almost periodic solutions of almost periodic differential equations, J. Austral. Math. Soc. 17 (1974), 332-344. MR 0357979 (50:10444)

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DOI: https://doi.org/10.1090/S0002-9939-1986-0826492-4
Article copyright: © Copyright 1986 American Mathematical Society

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