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On periodic solutions of countable systems of linear and quasilinear difference equations with periodic coefficients

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Abstract

We present conditions for the existence of periodic solutions of linear difference equations with periodic coefficients in spaces of bounded number sequences. In the case where the generating linear equation has a unique periodic solution, we indicate sufficient conditions for the existence of a periodic solution of a quasilinear difference equation.

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References

  1. V. G. Boltyanskii,Optimal Control of Discrete Systems [in Russian] Nauka, Moscow 1973.

    Google Scholar 

  2. A. Halanay and D. Wexler,Teoria Calitativa a Sistemelor cu Impulsuri [in Italian] Editura Academiei, Bucuresti 1968.

    MATH  Google Scholar 

  3. Yu. A. Mitropols’kii, A. M. Samoilenko, and D. I. Martynyuk,Systems of Evolution Equations with Periodic and Conditional-Periodic Coefficients [in Russian] Naukova Dumka, Kiev 1984.

    Google Scholar 

  4. D. I. Martynyuk,Lectures on Qualitative Theory of Difference Equations [in Russian] Naukova Dumka, Kiev 1972.

    Google Scholar 

  5. D. I. Martynyuk, N. V. Mironov, and L. V. Kharabovskaya, “A numerical-analytic method of investigation of periodic solutions of nonlinear difference equations,” in:Differential-Difference Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1971), pp. 45–58.

    Google Scholar 

  6. D.I. Martynyuk and N. A. Perestyuk, “On the reducibility of linear systems of difference equations with quasiperiodic coefficients,”Vych. Prikl. Mat.,23, 116–127 (1974).

    Google Scholar 

  7. D. I. Martynyuk and N. A. Perestyuk, “On the reducibility of difference equations on a torus,”Vych. Prikl. Mat.,26, 42–48 (1975).

    Google Scholar 

  8. A. M. Samoilenko, D. I. Martynyuk, and N. A. Perestyuk, “On the existence of invariant tori of systems of difference equations,”Differents. Uravn.,9, 1904–1910 (1973).

    Google Scholar 

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Authors and Affiliations

  1. Kamenets-Podol’sk Pedagogical Institute, Kamenets-Podorsk

    Yu. V. Teplinskii

  2. Ukrainian Pedagogical University, Kiev

    M. V. Samoilenko

Authors
  1. Yu. V. Teplinskii
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  2. M. V. Samoilenko
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Teplinskii, Y.V., Samoilenko, M.V. On periodic solutions of countable systems of linear and quasilinear difference equations with periodic coefficients. Ukr Math J 48, 1299–1308 (1996). https://doi.org/10.1007/BF02383875

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  • DOI: https://doi.org/10.1007/BF02383875

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