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Nonlinear Oscillations

, Volume 12, Issue 4, pp 559–573 | Cite as

Continuous solutions of nonlinear functional difference equations and their properties

  • H. P. Pelyukh
  • O. A. Sivak
Article

We establish conditions for the existence of continuous bounded solutions of systems of nonlinear functional difference equations and study their properties.

Keywords

Periodic Solution Difference Equation Vector Function Continuous Solution Ukrainian National Academy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. D. Birkhoff, “General theory of linear difference equations,” Trans. Amer. Math. Soc., 12, 243–284 (1911).MATHMathSciNetGoogle Scholar
  2. 2.
    G. D. Birkhoff, “Formal theory of irregular linear difference equations,” Acta Math., 54, 205–246 (1930).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    R. D. Carmichael, “Linear difference equations and their analytic solutions,” Trans. Amer. Math. Soc., 12, 99–134 (1911).MATHMathSciNetGoogle Scholar
  4. 4.
    C. R. Adams, “On the irregular cases of linear ordinary difference equations,” Trans. Amer. Math. Soc., 30, No. 3, 507–541 (1928).MATHMathSciNetGoogle Scholar
  5. 5.
    W. J. Tzjitzinsky, “Analytic theory of linear q-difference equations,” Acta Math., 61, 1–38 (1933).CrossRefGoogle Scholar
  6. 6.
    H. P. Pelyukh and O. A. Sivak, “Investigation of the structure of the set of continuous solutions of systems of linear functional difference equations,” Nelin. Kolyvannya, 12, No. 3, 307–335 (2009).MathSciNetGoogle Scholar
  7. 7.
    O. A. Sivak, “On the existence of solutions of systems of linear functional difference equations continuous for tR and their properties,” in: Proceedings of the Institute of Mathematics of the Ukrainian National Academy of Sciences [in Ukrainian], Vol. 6, No. 2, Kiev (2009), pp. 450–459.Google Scholar
  8. 8.
    G. P. Pelyukh, “On the structure of continuous solutions of one class of nonlinear difference equations,” Differents. Uravn., No. 6, 1083–1085 (1994).MathSciNetGoogle Scholar
  9. 9.
    G. P. Pelyukh, “On periodic solutions of difference equations with continuous argument,” Ukr. Mat. Zh., 48, No. 1, 140–144 (1996).CrossRefMathSciNetGoogle Scholar
  10. 10.
    G. P. Pelyukh, “On the existence of periodic solutions of nonlinear difference equations,” Ukr. Mat. Zh., 54, No. 12, 1626–1633 (2002).MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  • H. P. Pelyukh
    • 1
  • O. A. Sivak
    • 1
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine

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