Skip to main content
SpringerLink
Log in

Periodic and Almost Periodic Solutions of Difference Equations in Metric Spaces

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We establish conditions for the existence of almost periodic and periodic solutions of almost periodic difference equations with discrete argument in a metric space without using the -classes of these equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Bochner, “Beitrage zur Theorie der fastperiodischen. I Teil,” Math. Ann., 96, 119–147 (1927); S. Bochner, “Beitrage zur Theorie der fastperiodischen. II Teil,” Math. Ann., 96, 383–409 (1927).

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

    MATH  Google Scholar 

  3. É. Mukhamadiev, “On the invertibility of functional operators in a space of functions bounded on the axis,” Mat. Zametki, 11, No. 3, 269–274 (1972).

    MathSciNet  Google Scholar 

  4. É. Mukhamadiev, “Investigations into the theory of periodic and bounded solutions of differential equations,” Mat. Zametki, 30, No. 3, 443–460 (1981).

    MathSciNet  MATH  Google Scholar 

  5. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Ukrainian], Vyshcha Shkola, Kyiv (1974).

    Google Scholar 

  6. L. Amerio, “Soluzioni quasiperiodiche, o limital, di sistemi differenziali non lineari quasi-periodici, o limitati,” Ann. Mat. Pura Appl., 39, 97–119 (1955).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    MATH  Google Scholar 

  8. V. Yu. Slyusarchuk, “Conditions of almost periodicity for bounded solutions of nonlinear difference equations with continuous argument,” Nelin. Kolyv., 16, No. 1, 118–124 (2013); English translation: J. Math. Sci., 197, No. 1, 122–128 (2013).

  9. V.Yu. Slyusarchuk, “Conditions of almost periodicity for bounded solutions of nonlinear difference equations with continuous argument,” J. Math. Sci., 197, No. 1, 122–128 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  10. V. Yu. Slyusarchuk, “Conditions for the existence of almost periodic solutions of nonlinear differential equations in Banach spaces,” Ukr. Mat. Zh., 65, No. 2, 307–312 (2013); English translation: Ukr. Math. J., 65, No. 2, 341–347 (2013).

  11. V. Yu. Slyusarchuk, “A criterion of existence of almost periodic solutions of nonlinear equations without using the -classes of these equations,” Bukov. Mat. Zh., 1, No. 1–2, 136–138 (2013).

    MATH  Google Scholar 

  12. V. Yu. Slyusarchuk, “Investigation of almost periodic difference equations with continuous argument without using the -classes of these equations,” Bukov. Mat. Zh., 1, No. 3–4, 137–143 (2013).

    MATH  Google Scholar 

  13. V. Yu. Slyusarchuk, “Conditions for the existence of almost periodic solutions of nonlinear difference equations with discrete argument,” Nelin. Kolyv., 16, No. 3, 416–425 (2013); English translation: J. Math. Sci., 201, No. 3, 391–399 (2013).

  14. V. Yu. Slyusarchuk, “Conditions for almost periodicity of bounded solutions of nonlinear differential equations unsolvable with respect to the derivative,” Ukr. Mat. Zh., 66, No. 3, 384–393 (2014); English translation: Ukr. Math. J., 66, No. 3, 432–442 (2014).

  15. J. Favard, “Sur les Kequations différentielles linéaires à coefficients presque-péisriodiques,” Acta Math., 51, 31–81 (1928).

    Article  MathSciNet  Google Scholar 

  16. V. E. Slyusarchuk, “Invertibility of almost periodic c-continuous functional operators,” Mat. Sb., 116(158), No. 4(12), 483–501 (1981).

  17. V. E. Slyusarchuk, “Invertibility of nonautonomous functional-differential operators,” Mat. Sb., 130(172), No. 1(5), 86–104 (1986).

  18. V. E. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of nonautonomous functional-differential operators,” Mat. Zametki, 42, No. 2, 262–267 (1987).

    MathSciNet  MATH  Google Scholar 

  19. L. Amerio, “Sull equazioni differenziali quasi-periodiche astratte,” Ric. Mat., 30, 288–301 (1960).

    MATH  Google Scholar 

  20. V. V. Zhikov, “Proof of the Favard theorem on the existence of an almost periodic solution in the case of an arbitrary Banach space,” Mat. Zametki, 23, No. 1, 121–126 (1978).

    MathSciNet  Google Scholar 

  21. V. Yu. Slyusarchuk, “Conditions for the existence of bounded solutions of nonlinear difference equations,” Nauk. Visn. Cherniv. Univ., Ser. Mat., Issue 454, 88–94 (2009).

  22. V. Yu. Slyusarchuk, “Method of local linear approximation in the theory of bounded solutions of nonlinear difference equations,” Nelin. Kolyv., 12, No. 3, 368–378 (2009); English translation: Nonlin. Oscillations, 12, No. 3, 380–391 (2009).

  23. V. Yu. Slyusarchuk, “Method of locally linear approximation of nonlinear difference operators by weakly regular operators,” Nelin. Kolyv., 15, No. 4, 112–126 (2012); English translation: J. Math. Sci., 187, No. 4, 494–510 (2012).

Download references

Author information

Authors and Affiliations

  1. National University of Water Management and Nature Resources, Soborna Str. 11, Rivne, 33000, Ukraine

    V. Yu. Slyusarchuk

Authors
  1. V. Yu. Slyusarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Yu. Slyusarchuk.

Additional information

Translated from Neliniini Kolyvannya, Vol. 18, No. 1, pp. 112–119, January–March, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slyusarchuk, V.Y. Periodic and Almost Periodic Solutions of Difference Equations in Metric Spaces. J Math Sci 215, 387–394 (2016). https://doi.org/10.1007/s10958-016-2845-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-016-2845-7

Keywords

Search

Navigation