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On linear homogeneous almost periodic systems that satisfy the Favard condition

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Abstract

We prove the existence of a linear homogeneous almost periodic system of differential equations that has nontrivial bounded solutions and is such that all systems from a certain neighborhood of it have no nontrivial almost periodic solutions.

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References

  1. B. M. Levitan, Almost Periodic Functions [in Russian], Gostekhizdat, Moscow (1953).

    Google Scholar 

  2. K. J. Palmer, “On bounded solutions of almost periodic linear differential systems,” J. Math. Anal. Appl., 103, No. 1, 16–25 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  3. R. J. Sacker and G. R. Sell, “Existence of dichotomies and invariant splittings for linear differential systems III,” J. Different. Equats., 22, No. 4, 479–522 (1976).

    Google Scholar 

  4. L. H. Loomis, An Introduction to Abstract Harmonic Analysis, New York, Nostrand (1953).

    MATH  Google Scholar 

  5. B. F. Bylov, R. É. Vinigrad, V. Ya. Lin, and O. V. Lokutsievskii, “On topological grounds of anomalous behavior of some almost periodic systems,” in: Problems of the Asymptotic Theory of Nonlinear Oscillations [in Russian], Naukova Dumka, Kiev (1977), pp. 54–61.

    Google Scholar 

  6. Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  7. R. J. Sacker and G. R. Sell, “A spectral theory for linear differential systems,” J. Different. Equat., 27, No. 3, 320–358 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  8. V. I. Tkachenko, “On linear almost periodic systems with bounded solutions,” Bull. Austral. Math. Soc., 55, 177–184 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. M. Samoilenko, “Quasiperiodic solutions of systems of linear algebraic equations with quasiperiodic coefficients,” in: Analytic Methods for the Investigation of Solutions of Nonlinear Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1975), pp. 5–26.

    Google Scholar 

  10. A. M. Samoilenko, Elements of the Mathematical Theory of Multifrequency Oscillations. Invariant Tori [in Russian], Nauka, Moscow (1987).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. I. Tkachenko

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  1. V. I. Tkachenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 409–413, March, 1998.

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Tkachenko, V.I. On linear homogeneous almost periodic systems that satisfy the Favard condition. Ukr Math J 50, 464–469 (1998). https://doi.org/10.1007/BF02528810

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  • DOI: https://doi.org/10.1007/BF02528810

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