Skip to main content
Springer Nature Link
Log in

On the Existence of Local Smooth Solutions of Systems of Nonlinear Functional Equations with Deviations Dependent on Unknown Functions

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We obtain conditions for the existence of a local differentiable solution of a system of nonlinear functional equations with nonlinear deviations of an argument.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

    Google Scholar 

  2. M. Kuczma, Functional Equations in a Single Variable PWN, Warsaw (1968).

    Google Scholar 

  3. M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations, Encyclopedia of Mathematics and Its Applications Vol. 32, Cambridge University Press, Cambridge (1990).

    Google Scholar 

  4. K. Baron and W. Jarczyk, Recent Results on Functional Equations in a Single Variable, Perspectives and Open Problems Silesian University Press (1999).

  5. G. R. Belitskii, Normal Forms, Invariants, and Local Mappings [in Russian], Naukova Dumka, Kiev (1979).

    Google Scholar 

  6. L. P. Kuchko, “Local solvability of functional equations and existence of invariant manifolds,” Sib. Mat. Zh. 18, No. 2, 327–339 (1977).

    Google Scholar 

  7. P. Hartman, “On local homeomorphism of Euclidean spaces,” Bol. Soc. Mat. Mexic. 5, 220–241 (1960).

    Google Scholar 

  8. J. Moser, “The analytic invariants of an area-preserving mapping near a hyperbolic fixed point,” Commun. Pure Appl. Math. 9, 673–692 (1956).

    Google Scholar 

  9. S. Sternberg, “On the behavior of invariant curves near a hyperbolic point of a surface transformation,” Amer. J. Math. 77, 526–534 (1955).

    Google Scholar 

  10. M. Urabe, “Invariant varieties for finite transformation,” J. Sci. Hiroshima Univ., Ser. A 16, 47–55 (1952).

    Google Scholar 

  11. G. P. Pelyukh, “Representation of solutions of difference equations with continuous argument,” Differents. Uravn. 32, No. 2, 304–312 (1996).

    Google Scholar 

  12. H. Poincaré, On Curves Defined by Differential Equations [Russian translation], Gostekhteoretizdat, Moscow (1947).

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    G. P. Pelyukh

Authors
  1. G. P. Pelyukh
    View author publications

    You can also search for this author inPubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pelyukh, G.P. On the Existence of Local Smooth Solutions of Systems of Nonlinear Functional Equations with Deviations Dependent on Unknown Functions. Ukrainian Mathematical Journal 53, 75–90 (2001). https://doi.org/10.1023/A:1010440917829

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010440917829

Keywords