Skip to main content
SpringerLink
Log in

Reducibility and Generalized Reducibility of Linear Differential Systems with a Real Multiplier Parameter

  • ORDINARY DIFFERENTIAL EQUATIONS
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We construct a pair of mutually reducible linear differential systems with bounded continuous coefficients on the time half-line with the following property: there exists a countable set of real numbers such that, for each number in this set, the systems obtained by multiplying the coefficient matrices of the original systems by that number cannot be reduced to each other but are reducible to each other in the generalized sense.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Similar content being viewed by others

REFERENCES

  1. Lyapunov, A.M., Sobr. soch. v 6 t. T. 2. Obshchaya zadacha ob ustoichivosti dvizheniya (Collected Papers in 6 Vols. Vol. 2. General Problem of Stability of Motion), Moscow–Leningrad: Gos. Izd. Tekh.-Teor. Lit., 1956.

    Google Scholar 

  2. Basov, V.P., On the structure of the solution to a regular system, Vestn. Leningr. Univ. Ser. Mat. Fiz. Khim., 1952, no. 12, pp. 3–8.

  3. Grobman, D.M., Characteristic indices of systems close to linear ones, Mat. Sb., 1952, vol. 30, no. 1, pp. 121–166.

    MathSciNet  Google Scholar 

  4. Bogdanov, Yu.S., To the theory of systems of linear differential equations, Dokl. Akad. Nauk SSSR, 1955, vol. 104, no. 6, pp. 813–814.

    MathSciNet  Google Scholar 

  5. Adrianova, L.Ya., Vvedenie v teoriyu lineinykh sistem differentsial’nykh uravnenii (Introduction to the theory of linear systems of differential equations), St. Petersburg: S.-Peterb. Gos. Univ., 1992.

    Google Scholar 

  6. Barabanov, E.A., Kinematic similarity of linear differential systems with a parametric coefficient multiplying the derivative, J. Math. Sci., 2015, vol. 210, no. 2, pp. 135–147.

    Article  MathSciNet  Google Scholar 

  7. Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Heidelberg: Springer-Verlag, 1959. Translated under the title: Asimptoticheskoe povedenie i ustoichivost’ reshenii obyknovennykh differentsial’nykh uravnenii, Moscow: Mir, 1964.

    Book  Google Scholar 

  8. Khudyakova, P.A., On the generalized kinematic similarity of matrix-valued functions with a real multiplier parameter, in Mater. Mezhdunar. mat. konf. “Shestye Bogdanovskie chteniya po obyknovennym differentsial’nym uravneniyam” v 2 ch. Ch. 1. (Proc. Int. Math. Conf. “Sixth Bogdanov Readings on Ordinary Differential Equations”, in 2 Parts. Part 1), Minsk, December 7–10, 2015, pp. 48–50.

  9. Izobov, N.A. and Makarov, E.K., On Lyapunov irregular linear systems with a parameter multiplying the derivative, Differ. Uravn., 1988, vol. 24, no. 11, pp. 1870–1880.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan

    T. M. Aldibekov

Authors
  1. T. M. Aldibekov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. M. Aldibekov.

Additional information

Translated by V. Potapchouck

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aldibekov, T.M. Reducibility and Generalized Reducibility of Linear Differential Systems with a Real Multiplier Parameter. Diff Equat 56, 1–6 (2020). https://doi.org/10.1134/S0012266120010012

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266120010012

Search

Navigation