Advertisement

Journal of Mathematical Sciences

, Volume 243, Issue 2, pp 240–278 | Cite as

Asymptotic Properties of the Solutions of Functional-Differential Equation with Linearly Transformed Argument

  • G. P. Pelyukh
  • D. V. Bel’skii
Article
  • 1 Downloads

We establish new properties of the solutions of functional-differential equation with linearly transformed argument.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Kato and J. B. McLeod, “The functional-differential equation;” y′(x) = ayx) + by(x) Bull. Amer. Math. Soc., 77, 891–937 (1971).MathSciNetCrossRefGoogle Scholar
  2. 2.
    N. G. de Bruijn, “The difference-differential equation F′(x) = e 𝛼x+𝛽F(x–1) I, II,” Nederl. Akad. Wetensch. Proc. Ser. A 56. Indag. Math., 15, 449–464 (1953).Google Scholar
  3. 3.
    P. O. Frederickson, “Series solutions for certain functional-differential equations,” in: Lecture Notes in Mathematics, 243 (1971), pp. 249–254.Google Scholar
  4. 4.
    G. P. Pelyukh and A. N. Sharkovskii, Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev (1974).Google Scholar
  5. 5.
    G. A. Derfel’, “Probabilistic method for a class of functional-differential equations,” Ukr. Mat. Zh.,41, No. 10, 1483–1491 (1989); English translation:Ukr. Math. J.,41, No. 10, 1137–1141 (1989).MathSciNetCrossRefGoogle Scholar
  6. 6.
    V. M. Polishchuk and A. N. Sharkovskii, “Representation of solutions of linear differential-difference equations of the neutral type,” Differents. Uravn.,9, No. 9, 1627–1645 (1973).MathSciNetGoogle Scholar
  7. 7.
    P. O. Frederickson, “Global solutions to certain nonlinear functional differential equations,” J. Math. Anal. Appl.,33, 355–358 (1971).MathSciNetCrossRefGoogle Scholar
  8. 8.
    I. Gumovski and C. Mira, Recurrences and Discrete Dynamic Systems, Springer, Berlin (1980).Google Scholar
  9. 9.
    D. V. Bel’skii and G. P. Pelyukh, “On the asymptotic properties of solutions of one functional-differential equation with linearly transformed argument,” Nelin. Kolyv.,16, No. 3, 291–313 (2013); English translation:J. Math. Sci.,201, No. 3, 263-287 (2014).MathSciNetCrossRefGoogle Scholar
  10. 10.
    G. P. Pelyukh and D. V. Bel’skii, “On the asymptotic properties of the solutions of a linear functional-differential equation of neutral type with constant coefficients and linearly transformed argument,” Nelin. Kolyv.,15, No. 4, 466–493 (2012); English translation: J. Math. Sci.,194, No. 4, 374–403 (2013).MathSciNetCrossRefGoogle Scholar
  11. 11.
    G. P. Pelyukh, “On the asymptotic properties of the solutions of systems of nonlinear functional-differential equations,” Differents. Uravn.,38, No. 1, 1–5 (2003).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • G. P. Pelyukh
    • 1
  • D. V. Bel’skii
    • 1
  1. 1.Institute of Mathematics, Ukrainian National Academy of SciencesKyivUkraine

Personalised recommendations