Skip to main content
SpringerLink
Log in

On the well-posedness of differential equations unsolved for the derivative

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We prove some results concerning solvability, estimates for solutions, and well-posed solvability of equations with conditionally covering mappings. These results are applied to the analysis of differential equations unsolved for the derivative.

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. Arutyunov, A.V., Covering Mappings in Metric Spaces, and Fixed Points, Dokl. Akad. Nauk, 2007, vol. 416, no. 2, pp. 151–155.

    Google Scholar 

  2. Arutyunov, A., Avakov, E., Gel’man, B., et al., Locally Covering Maps in Metric Spaces and Coincidence Points, J. Fixed Points Theory Appl., 2009, vol. 5, no. 1, pp. 105–127.

    Article  MathSciNet  MATH  Google Scholar 

  3. Arutyunov, A.V., Stability of Coincidence Points and Properties of Covering Mappings, Mat. Zametki, 2009, vol. 86, no. 2, pp. 163–169.

    MathSciNet  Google Scholar 

  4. Arutyunov, A.V., Zhukovskiy, E.S, and Zhukovskiy, S.E., Covering Mappings and Well-Posedness of Nonlinear Volterra Equations, Nonlinear Anal., 2011, doi:10.1016/j.na. 2011.03.038.

  5. Arutyunov, A.V., Avakov, E.R., and Zhukovskii, E.S., Covering Mappings and Their Applications to Differential Equations Unsolved for the Derivative, Differ. Uravn., 2009, vol. 45, no. 5, pp. 613–634.

    MathSciNet  Google Scholar 

  6. Arutyunov, A.V. and Zhukovskii, S.E., Local Stability of Control Systems with Mixed Constraints, Differ. Uravn., 2010, vol. 46, no. 11, pp. 1561–1570.

    Article  MathSciNet  MATH  Google Scholar 

  7. Arutyunov, A.V. and Zhukovskiy, S.E., Existence of Local Solutions in Constrained Dynamical Systems, Appl. Anal., 2011, vol. 90. Iss. 6, pp. 889–898.

    Article  MathSciNet  Google Scholar 

  8. Zhukovskii, E.S. and Pluzhnikova, E.A., On a Certain Method for the Investigation of the Solvability of Boundary Value Problems for Differential Equations, Vestn. Tambov. Univ. Estestv. Tekhn. Nauk, 2010, vol. 15, no. 6, pp. 1673–1674.

    Google Scholar 

  9. Zhukovskii, E.S. and Zhukovskaya, T.V., On the Solvability of a Delay Differential Equation That Is Unsolved for the Derivative, Vestn. Tambov. Univ. Estestv. Tekhn. Nauk, 2011, vol. 16, no. 1, pp. 67–69.

    Google Scholar 

  10. Mordukhovich, B.S. and Wang, B., Restrictive Metric Regularity and Generalized Differential Calculus in Banach Spaces, Maths. Math. Sci., 2004, vol. 50, pp. 2650–2683.

    Google Scholar 

  11. Zabreiko, P.P., Koshelev, A.I., Krasnosel’skii, M.A., et al., Integral’nye uravneniya (Integral Equations), Moscow, 1968.

  12. Warga, J., Optimal Control of Differential and Functional Equations, New York: Academic, 1972. Translated under the title Optimal’noe upravlenie differentsial’nymi i funktsional’nymi uravneniyami, Moscow, 1977.

    MATH  Google Scholar 

  13. Filippov, A.F., Vvedenie v teoriyu differentsial’nykh uravnenii (Introduction to the Theory of Differential Equations), Moscow, 2004.

  14. Arutyunov, A.V. and Zhukovskii, S.E., Existence of Inverse Mappings and Their Properties, Tr. Mat. Inst. Steklova, 2010, vol. 271, pp. 9–19.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Moscow, Russia

    A. V. Arutyunov, E. S. Zhukovskii & S. E. Zhukovskii

  2. Tambov State University, Tambov, Russia

    A. V. Arutyunov, E. S. Zhukovskii & S. E. Zhukovskii

Authors
  1. A. V. Arutyunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. S. Zhukovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. E. Zhukovskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © A.V. Arutyunov, E.S. Zhukovskii, S.E. Zhukovskii, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 11, pp. 1523–1537.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arutyunov, A.V., Zhukovskii, E.S. & Zhukovskii, S.E. On the well-posedness of differential equations unsolved for the derivative. Diff Equat 47, 1541–1555 (2011). https://doi.org/10.1134/S0012266111110012

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266111110012

Keywords

Search

Navigation