Siberian Mathematical Journal

, Volume 46, Issue 3, pp 417–430 | Cite as

On Differential Equations with Retarded Argument

  • G. V. Demidenko
  • V. A. Likhoshvai
Article

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.

Keywords

systems with infinitely many ordinary differential equations differential equation with retarded argument 

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References

  1. 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
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    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).MathSciNetGoogle Scholar
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    Godunov S. K., Ordinary Differential Equations with Constant Coefficients [in Russian], Novosibirsk Univ., Novosibirsk (1994).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • G. V. Demidenko
    • 1
  • V. A. Likhoshvai
    • 2
  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Institute of Cytology and GeneticsNovosibirskRussia

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