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Conditionally Periodic Solutions of an Inhomogeneous Linear System Of Differential Equations with Conditionally Periodic Coefficients

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Abstract

We study the existence of a conditionally periodic solution of a linear system with a Stepanov conditionally periodic inhomogeneity. We prove that if this system has a bounded solution, then almost every system in its H-class has a bounded Besicovitch conditionally periodic solution.

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References

  1. Besicovitch, A.S., Almost Periodic Functions, New York: Dover, 1954.

    MATH  Google Scholar 

  2. Levitan, B.M., Pochti-periodicheskie funktsii (Almost Periodic Functions), Moscow: Gos. Izd. Tekhn. Teor. Lit., 1953.

    MATH  Google Scholar 

  3. Samoilenko, A.M., Elementy matematicheskoi teorii mnogochastotnykh kolebanii (Elements of Mathematical Theory of Multifrequency Oscillations), Moscow: Nauka, 1987.

    Google Scholar 

  4. Massera, J. and Shäffer, J., Linear Differential Equations and Function Spaces, New York: Academic, 1966. Translated under the title Lineinye differentsial’nye uravneniya i funktsional’nye prostranstva, Moscow: Mir, 1970.

    Google Scholar 

  5. Levitan, B.M. and Zhikov, V.V., Pochti-periodicheskie funktsii i differentsial’nye uravneniya (Almost Periodic Functions and Differential Equations) Moscow: Mosk. Gos. Univ., 1978.

    MATH  Google Scholar 

  6. Daletskii, Yu.L. and Krein, M.G., Ustoichivost’ reshenii differentsial’nykh uravnenii v banakhovom prostranstve (Stability of Solutions of Differential Equations in a Banach Space), Moscow: Nauka, 1970.

    Google Scholar 

  7. Levin, V.L., Measurable selections of multivalued mappings with bianalytic graph and σ-compact values, Trans. Moscow Math. Soc. 1993, pp. 1–22.

    Google Scholar 

  8. Kozlov, Yu.D., O privodimosti sistemy l.d.u. s uslovno-periodicheskimi koeffitsientami (Reducibility of a system of linear differential equations with conditionally periodic coefficients), Available from VINITI, 1995, Yekaterinburg, no. 1278–V95.

    Google Scholar 

  9. Kozlov, Yu.D., On the dichotomy of a system of linear differential equations with conditionally periodic coefficients, Differ. Equations, 2013, vol. 49, no. 3, pp. 282–287.

    Article  MathSciNet  MATH  Google Scholar 

  10. Dunford, N. and Schwartz, J.T., Linear Operators: General Theory, New York: Interscience, 1958. Translated under the title Lineinye operatory. Obshchaya teoriya, Moscow: Editorial URSS, 2004.

    MATH  Google Scholar 

  11. D’yachenko, M.I., Some problems in the theory of multiple trigonometric series, Russ. Math. Surveys, 1992, vol. 47, no. 5, pp. 103–171.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kornfel’d, N.P., Sinai, Ya.G., and Fomin, S.V., Ergodicheskaya teoriya (Ergodic Theory), Moscow: Nauka, 1980.

    Google Scholar 

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Authors and Affiliations

  1. Ural Federal University, Yekaterinburg, 620002, Russia

    Yu. D. Kozlov

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  1. Yu. D. Kozlov
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Correspondence to Yu. D. Kozlov.

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Original Russian Text © Yu.D. Kozlov, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 12, pp. 1593–1598.

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Kozlov, Y.D. Conditionally Periodic Solutions of an Inhomogeneous Linear System Of Differential Equations with Conditionally Periodic Coefficients. Diff Equat 53, 1543–1548 (2017). https://doi.org/10.1134/S0012266117120023

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  • DOI: https://doi.org/10.1134/S0012266117120023

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