Skip to main content
SpringerLink
Log in

On the behavior of solutions of linear functional differential equations with constant coefficients and linearly transformed argument in neighborhoods of singular points

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish new properties of C 1 (0, + ∞)-solutions of the linear functional differential equation \(\dot x(t) = ax(t) + bx(qt) + cx(qt)\) in the neighborhoods of the singular points t = 0 and t = + ∞.

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. T. Kato and J. B. McLeod, “The functional-differential equation y′ (x) = a y (λx) + b y (x),” Bull. Amer. Math. Soc., 77, 891–937 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  2. N. G. de Bruijn, “The difference-differential equation y′(x)=ay(λx)+by(x). I, II,” Ned. Akad. Wetensch. Proc., Ser. A. Math., 15, 449–464 (1953).

    Google Scholar 

  3. P. O. Frederickson, “Series solutions for certain functional-differential equations,” Lect. Notes Math., 243, 249–254 (1971).

    MATH  MathSciNet  Google Scholar 

  4. G. P. Pelyukh and A. N. Sharkovskii, Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev (1974).

    Google Scholar 

  5. G. A. Derfel’, “Probability method for the investigation of one class of functional differential equations,” Ukr. Mat. Zh., 41, No. 10, 12–16 (1989).

    MathSciNet  Google Scholar 

  6. D. V. Bel’skii, “On the asymptotic properties of solutions of linear functional differential equations with constant coefficients and linearly transformed argument,” Nelin. Kolyvannya, 7, No. 1, 48–52 (2004).

    MathSciNet  Google Scholar 

  7. I. Gumowski and C. Mira, Recurrences and Discrete Dynamic Systems, Springer, Berlin (1980).

    MATH  Google Scholar 

  8. J. Hale, Theory of Functional Differential Equations, Springer, Berlin (1977).

    MATH  Google Scholar 

  9. V. G. Kurbatov, Linear Difference-Differential Equations [in Russian], Voronezh University, Voronezh (1990).

    MATH  Google Scholar 

  10. V. Yu. Slyusarchuk, Absolute Stability of Dynamical Systems with Aftereffect [in Ukrainian], UDUVGP, Rivne (2003).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    G. P. Pelyukh & D. V. Bel’skii

Authors
  1. G. P. Pelyukh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. V. Bel’skii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1668–1676, December, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pelyukh, G.P., Bel’skii, D.V. On the behavior of solutions of linear functional differential equations with constant coefficients and linearly transformed argument in neighborhoods of singular points. Ukr Math J 57, 1957–1967 (2005). https://doi.org/10.1007/s11253-006-0041-5

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-006-0041-5

Keywords

Search

Navigation