Skip to main content
SpringerLink
Log in

On Differential Equations with Retarded Argument

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

We study the limit properties of solutions to one class of systems of differential equations as the number of equations and some parameters tend to infinity. We establish a close connection between solutions to these systems and differential equations with retarded argument. Our convergence theorems provide a new method for approximation of solutions to nonlinear differential equations with retarded argument.

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. Likhoshvai V. A., Fadeev S. I., Demidenko G. V., and Matushkin Yu. G., “Modeling by a delay equation of multiparae synthesis without bifurcation,” Sibirsk. Zh. Industr. Mat., 7, No.1, 73–94 (2004).

    Google Scholar 

  2. Demidenko G. V., Kolchanov N. A., Likhoshvai V. A., Matushkin Yu. G., and Fadeev S. I., “Mathematical modeling of regulator contours of gene nets,” Zh. Vychisl. Mat. i Mat. Fiziki, 44, No.12, 2276–2295 (2004).

    MathSciNet  Google Scholar 

  3. Godunov S. K., Ordinary Differential Equations with Constant Coefficients [in Russian], Novosibirsk Univ., Novosibirsk (1994).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    G. V. Demidenko

  2. Institute of Cytology and Genetics, Novosibirsk, Russia

    V. A. Likhoshvai

Authors
  1. G. V. Demidenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. A. Likhoshvai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text Copyright © 2005 Demidenko G. V. and Likhoshvai V. A.

The authors were supported by the Russian Foundation for Basic Research (Grants 03-01-00328, 03-04-48506, 03-04-48829, 03-07-96833, 04-01-00458, 05-04-49068, and 05-07-90274), the Integration Grant of the Siberian Branch of the Russian Academy of Sciences (No. 119 and 148), the Program “Development of the Scientific Potential of Higher School” of the Ministry for Education of the Russian Federation (Grant 8273), and NSF:FIBR (Grant EF-0330786).

__________

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 538–552, May–June, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Demidenko, G.V., Likhoshvai, V.A. On Differential Equations with Retarded Argument. Sib Math J 46, 417–430 (2005). https://doi.org/10.1007/s11202-005-0045-7

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-005-0045-7

Keywords

Search

Navigation