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On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems

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Ukrainian Mathematical Journal Aims and scope

We study sufficient conditions for the existence of bounded solutions of linear extensions of the dynamical systems.

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References

  1. O. Perron, “Die Stabilitatsfrage bei Differentialgleichungen,” Math. Z., 32, No. 4, 703 – 728 (1930).

    Article  MATH  MathSciNet  Google Scholar 

  2. Yu. A. Mitropol’skii, A. M. Samoilenko, and V. L. Kulik, Investigation of the Dichotomy of Linear Systems of Differential Equations by Using the Lyapunov Function [in Russian], Naukova Dumka, Kiev (1990).

    Google Scholar 

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

  4. I. U. Bronshtein and A. Ya. Kopanskii, Invariant Manifolds and Normal Forms [in Russian], Shtiintsa, Kishinev (1992).

    Google Scholar 

  5. A. M. Samoilenko and Yu. V. Teplins’kyi, Elements of the Mathematical Theory of Evolutionary Equations in Banach Spaces [in Ukrainian], Preprint, Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2008).

  6. V. E. Slyusarchuk, Invertibility of Nonlinear Difference Operators [in Ukrainian], National University of Water Industry and Nature Management, Rivne (2005).

    Google Scholar 

  7. Y. Latushkin, “Green’s function, continual weighed composition operators along trajectories, and hyperbolicity of linear extensions for dynamical systems,” J. Dynam. Different. Equat., 6, No. 1, 1–21 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Mane, “Quasi-Anosov diffeomorphisms and hyperbolic manifolds,” Trans. Amer. Math. Soc., 229, No. 2, 351–370 (1977).

    MATH  MathSciNet  Google Scholar 

  9. V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow (1947).

    Google Scholar 

  10. J. Jarnik and J. Kurzweil, “On invariant sets and invariant manifolds of differential equations,” J. Different. Equat., 6, No. 2, 247–263 (1969).

    Article  MATH  MathSciNet  Google Scholar 

  11. V. I. Oseledets, “Multiplicative ergodic theorem. Characteristic Lyapunov indices for dynamical systems,” Tr. Moscow Mat. Obshch., 19, 179–210 (1968).

    Google Scholar 

  12. R. Johnson, K. Palmer, and G. Sell, “Ergodic properties of linear dynamical systems,” SIAM J. Math. Anal., 18, No. 1, 1–33 (1987).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. ”Kyiv Polytechnic Institute” Ukrainian National Technical University, Kyiv, Ukraine

    A. L. Grechko

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  1. A. L. Grechko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 604–611, May, 2010.

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Grechko, A.L. On sufficient conditions for the existence of bounded solutions of inhomogeneous linear extensions of dynamical systems. Ukr Math J 62, 691–700 (2010). https://doi.org/10.1007/s11253-010-0381-z

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  • DOI: https://doi.org/10.1007/s11253-010-0381-z

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