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Proceedings of the American Mathematical Society

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



Almost periodic solutions for a certain class of almost periodic systems

Author: George Seifert
Journal: Proc. Amer. Math. Soc. 84 (1982), 47-51
MSC: Primary 34C27
MathSciNet review: 633275
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Abstract: Using a result due to Medvedev [3], we obtain conditions under which systems of ordinary differential equations of the form $ x' = F(t,x,x) + G(t,x)$ where $ F$ and $ G$ are almost periodic in $ t$ will have unique almost periodic solutions with certain global stability properties and module containment. These conditions are compared to conditions for the existence, but not uniqueness, for such solutions obtained by Kartsatos in [2]. Both results, our as well as Kartsatos', are applied to a second order equation of Lienard type with almost periodic forcing.

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

  • [1] A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
  • [2] Athanassios G. Kartsatos, Almost periodic solutions to nonlinear systems, Boll. Un. Mat. Ital. (4) 9 (1974), 10–15 (English, with Italian summary). MR 0355201
  • [3] N. V. Medvedev, Certain criteria for the existence of bounded solutions of a system of differential equations, Differencial′nye Uravnenija 4 (1968), 1258–1264 (Russian). MR 0230979
  • [4] T. Yoshizawa, Stability theory and the existence of periodic solutions and almost periodic solutions, Springer-Verlag, New York-Heidelberg, 1975. Applied Mathematical Sciences, Vol. 14. MR 0466797

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Keywords: Almost periodic systems, almost periodic solutions
Article copyright: © Copyright 1982 American Mathematical Society