Skip to main content
SpringerLink
Log in

On the asymptotic equilibrium and asymptotic equivalence of differential equations in Banach spaces

  • Published:
Ukrainian Mathematical Journal Aims and scope

We present some conditions for the asymptotic equilibrium of nonlinear differential equations and, in particular, a linear inhomogeneous equation in Banach spaces. We also discuss analogous problems for a linear equation with unbounded operator. Some obtained results are applied to problems of asymptotic equivalence.

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. Nguyen The Hoan, “Asymptotic behavior of solutions of nonlinear systems of differential equations,” Differents. Uravn., 12, No. 4, 624–628 (1981).

    Google Scholar 

  2. E. V. Voskresenskii, “On the Cesari problem,” Differents. Uravn., 25, No. 9, 1480–1485 (1989).

    MathSciNet  Google Scholar 

  3. S. W. Seah, “Existence of solutions and asymptotic equilibrium of multivalued differential systems,” J. Math. Anal. Appl., 89, 648–663 (1982).

    Article  MATH  MathSciNet  Google Scholar 

  4. S. W. Seah, “Asymptotic equivalence of multivalued differential systems,” Boll. Unione Math. Ital. B, 17, 1124–1145 (1980).

    MATH  MathSciNet  Google Scholar 

  5. Nguyen Minh Man and Nguyen The Hoan, “On the asymptotic behavior of solutions of linear differential equations,” Ukr. Mat. Zh., 55, No. 4, 561–569 (2003).

    MATH  Google Scholar 

  6. M. A. Krasnosel’skii and S. G. Krein, “On the theory of differential equations in Banach spaces,” Tr. Semin. Funkts. Anal., 2 (1956).

  7. A. V. Balakrishnan, Introduction to Optimization Theory in a Hilbert Space [Russian translation], Mir, Moscow (1974).

    MATH  Google Scholar 

  8. B. P. Demidovich, Lectures on Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).

    Google Scholar 

  9. Yu. L. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Nguyen Trai, Hanoi, Vietnam

    Nguyen Sinh Bay, Nguyen The Hoan & Nguyen Minh Man

Authors
  1. Nguyen Sinh Bay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nguyen The Hoan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nguyen Minh Man
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 626–635, May, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bay, N.S., Hoan, N.T. & Man, N.M. On the asymptotic equilibrium and asymptotic equivalence of differential equations in Banach spaces. Ukr Math J 60, 716–729 (2008). https://doi.org/10.1007/s11253-008-0090-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-008-0090-z

Keywords

Search

Navigation