Skip to main content
Log in

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

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

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

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MathSciNet  Google Scholar 

  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).

  3. P. O. Frederickson, “Series solutions for certain functional-differential equations,” in: Lecture Notes in Mathematics, 243 (1971), pp. 249–254.

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

  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).

    Article  MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  7. P. O. Frederickson, “Global solutions to certain nonlinear functional differential equations,” J. Math. Anal. Appl.,33, 355–358 (1971).

    Article  MathSciNet  Google Scholar 

  8. I. Gumovski and C. Mira, Recurrences and Discrete Dynamic Systems, Springer, Berlin (1980).

  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).

    Article  MathSciNet  Google Scholar 

  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).

    Article  MathSciNet  Google Scholar 

  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).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Neliniini Kolyvannya, Vol. 21, No. 2, pp. 197–230, April–June, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pelyukh, G.P., Bel’skii, D.V. Asymptotic Properties of the Solutions of Functional-Differential Equation with Linearly Transformed Argument. J Math Sci 243, 240–278 (2019). https://doi.org/10.1007/s10958-019-04538-w

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-019-04538-w

Navigation