Skip to main content
SpringerLink
Log in

General conditions for the unique solvability of initial-value problem for nonlinear functional differential equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish general conditions for the unique solvability of the Cauchy problem for systems of nonlinear functional differential equations.

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. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional Differential Equations [in Russian], Moscow, Nauka (1991).

    MATH  Google Scholar 

  2. E. Bravyi, R. Hakl, and A. Lomtatidze, “Optimal conditions for unique solvability of the Cauchy problem for first-order linear functional differential equations,” Czech. Math. J., 52, No. 3, 513–530 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  3. R. Hakl, A. Lomtatidze, and B. Půža, “New optimal conditions for unique solvability of the Cauchy problem for first-order linear functional differential equations,” Math. Bohem., 127, No. 4, 509–524 (2002).

    MATH  MathSciNet  Google Scholar 

  4. A. N. Ronto, “Exact solvability conditions for the Cauchy problem for systems of first-order linear functional differential equations determined by (σ1, σ2, …, σn; τ)-positive operators,” Ukr. Math. J., 55, No. 11, 1853–1884 (2003).

    Article  MathSciNet  Google Scholar 

  5. N. Z. Dil’naya and A. N. Ronto, “Some new conditions for the solvability of the Cauchy problem for systems of linear functional differential equations,” Ukr. Math. J., 56, No. 7, 1033–1053 (2004).

    MathSciNet  Google Scholar 

  6. A. Rontó, “On the initial-value problem for systems of linear differential equations with argument deviations,” Miskolc Math. Notes, 6, No. 1, 105–127 (2005).

    MATH  MathSciNet  Google Scholar 

  7. R. Hakl, A. Lomtatidze, and B. Půža, “On nonnegative solutions of first-order scalar functional differential equations,” Mem. Different. Equat. Math. Phys., 23, 51–84 (2001).

    MATH  Google Scholar 

  8. A. M. Samoilenko, N. Z. Dil’na, and A. M. Ronto, “Solvability of the Cauchy problem for linear integro-differential equations with transformed argument,” Nelin. Kolyvannya, 8, No. 3, 388–403 (2005).

    MathSciNet  Google Scholar 

  9. M. A. Krasnosel’skii, E. A. Lifshits, Yu. V. Pokornyi, and V. Ya. Stetsenko, “Positive-invertible linear operators and solvability of nonlinear equations,” Dokl. Akad. Nauk Tadzhik. SSR, 17, No. 1, 12–14 (1974).

    Google Scholar 

  10. M. A. Krasnosel’skii and P. P. Zabreiko, Geometric Methods of Nonlinear Analysis [in Russian], Nauka, Moscow (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    N. Z. Dil’na & A. M. Ronto

Authors
  1. N. Z. Dil’na
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. M. Ronto
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 167–172, February, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dil’na, N.Z., Ronto, A.M. General conditions for the unique solvability of initial-value problem for nonlinear functional differential equations. Ukr Math J 60, 191–198 (2008). https://doi.org/10.1007/s11253-008-0051-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0051-6

Keywords

Search

Navigation