Skip to main content
SpringerLink
Log in

Some properties of solutions of systems of two linear first-order ordinary differential equations

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

Abstract

Using the representation of the general real solution of a system of two linear first-order equations via the imaginary component of the complex solution of the Riccati equation corresponding to this system, we prove some asymptotic properties of solutions of nonoscillating systems. We obtain necessary conditions for the Lyapunov stability of these systems.

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. 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.

    Book  MATH  Google Scholar 

  2. Hartman, Ph., Ordinary Differential Equations, New York, 1969. Translated under the title Obyknovennye differentsial’nye uravneniya, Moscow, 1970.

    Google Scholar 

  3. Sansone, G., Equazioni differenziali nel campo reale. Pt. 1, Bologna, 1948. Translated under the title Obyknovennye differentsial’nye uravneniya. T. 1, Moscow: Inostrannay Literatura, 1953.

    Google Scholar 

  4. Kiguradze, I.T. and Chanturiya, T.A., Asimptoticheskie svoistva reshenii neavtonomnykh obyknovennykh differentsial’nykh uravnenii (Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations), Moscow, 1990.

    Google Scholar 

  5. Sobol’, I.M., Investigation with the Aid of Polar Coordinates of the Asymptotic Behavior of Solutions of a Linear Differential Equation of the Second Order, Mat. Sb., 1951, vol. 28 (70), no. 3, pp. 707–714.

    MathSciNet  Google Scholar 

  6. Mirzov, D.D., Asymptotic Properties of the Solutions of Two-Dimensional Differential Systems, Differ. Uravn., 1977, vol. 13, no. 12, pp. 2188–2198.

    MATH  MathSciNet  Google Scholar 

  7. Gusarov, L.A., On the Approach to Zero of the Solutions of a Linear Differential Equation of the Second Order, Dokl. Akad. Nauk SSSR, 1950, vol. 71, no. 1, pp. 9–12.

    MATH  MathSciNet  Google Scholar 

  8. Egorov, A.I., Uravneniya Rikkati (Riccati Equations), Moscow, 2001.

    MATH  Google Scholar 

  9. Kamke, E.W.H., Differentialgleichungen, Leipzig, 1959. Translated under the title Spravochnik po obyknovennym differentsial’nym uravneniyam, Moscow, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Mathematics, National Academy of Sciences, Erevan, Armenia

    G. A. Grigoryan

Authors
  1. G. A. Grigoryan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. A. Grigoryan.

Additional information

Original Russian Text © G.A. Grigoryan, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 4, pp. 436–444.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grigoryan, G.A. Some properties of solutions of systems of two linear first-order ordinary differential equations. Diff Equat 51, 440–448 (2015). https://doi.org/10.1134/S0012266115040023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266115040023

Keywords

Search

Navigation