Skip to main content
SpringerLink
Log in

On the asymptotic behavior of solutions of nonlinear differential systems

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

Abstract

We obtain constructive conditions for the unique solvability of the singular problem dx/dt = f(t, x), x ∞ = 0, where f ∈ C (0,1)([0, ∞) × ℝn, ℝn).

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. Bogdanov, Yu.S. and Syroid, Yu.B., Differentsial’nye uravneniya (Differential Equations), Minsk: Vysh. Shkola, 1983.

    Google Scholar 

  2. Brekhovskikh, L.M., Volny v sloistykh sredakh (Waves in Layered Media), Moscow: Nauka, 1973.

    Google Scholar 

  3. Zubov, V.I., Lektsii po teorii upravleniya (Lectures in Control Theory), Moscow, Nauka, 1975.

    MATH  Google Scholar 

  4. Calogero, F., Variable Phase Approach to Potential Scattering, New York: Academic, 1967. Translated under the title Metod fazovykh funktsii v teorii potensial’nogo rasseyaniya, Moscow: Mir, 1972.

    MATH  Google Scholar 

  5. Kiguradze, I.T., Itogi Nauki Tekh. Ser. Sovrem. Probl. Mat. Noveish. Dostizh., 1987, vol. 30, pp. 3–103.

    MathSciNet  Google Scholar 

  6. Laptinskii, V.N., Vestsi Akad. Navuk Belarusi. Ser. Fiz.-Mat. Navuk, 1995, no. 2, pp. 12–16.

  7. Laptinskii, V.N., Differ. Uravn., 1996, vol. 32, no. 1, pp. 131–132.

    MathSciNet  Google Scholar 

  8. Laptinskii, V.N., Differ. Uravn., 1997, vol. 33, no. 2, pp. 275–277.

    MathSciNet  Google Scholar 

  9. Kantorovich, L.V. and Akilov, G.P., Funktsional’nyi analiz (Functional Analysis), Moscow: Nauka, 1977.

    Google Scholar 

  10. Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Berlin, 1959. Translated under the title Asimptoticheskoe povedenie i ustoichivost’ reshenii obyknovennykh differentsial’nykh uravnenii, Moscow, 1964.

  11. Demidovich, B.P., Lektsii po matematicheskoi teorii ustoichivosti (Lectures on Stability Theory), Moscow: Nauka, 1967.

    Google Scholar 

  12. Zabreiko, P.P. and Laptinskii, V.N., Dokl. Akad. Navuk Belarusi, 1997, vol. 41, no. 1, pp. 5–9.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Technology of Metals, National Academy of Sciences, Mogilev, Belarus

    V. N. Laptinskii

Authors
  1. V. N. Laptinskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.N. Laptinskii, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 2, pp. 205–210.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laptinskii, V.N. On the asymptotic behavior of solutions of nonlinear differential systems. Diff Equat 44, 213–218 (2008). https://doi.org/10.1134/S0012266108020080

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266108020080

Keywords

Search

Navigation