Almost periodic solutions for a certain class of almost periodic systems
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- by George Seifert PDF
- Proc. Amer. Math. Soc. 84 (1982), 47-51 Request permission
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
- A. M. Fink, Almost periodic differential equations, Lecture Notes in Mathematics, Vol. 377, Springer-Verlag, Berlin-New York, 1974. MR 0460799
- Athanassios G. Kartsatos, Almost periodic solutions to nonlinear systems, Boll. Un. Mat. Ital. (4) 9 (1974), 10–15 (English, with Italian summary). MR 0355201
- 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
- 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
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 47-51
- MSC: Primary 34C27
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633275-3
- MathSciNet review: 633275