Journal of Mathematical Sciences

, Volume 231, Issue 5, pp 587–597 | Cite as

On the Solutions of Oscillating-Type Countable Differential Systems with Slowly Varying Parameters

  • S. A. Shchogolev
  • V. V. Jashitova

For a countable quasilinear system of differential equations whose coefficients have the form of absolutely and uniformly convergent Fourier series with slowly varying coefficients and frequency, we obtain conditions for the existence of a partial solution of a similar structure. As a result, we establish conditions for the possibility of complete decomposition of a countable linear homogeneous differential system with coefficients of the same structure.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).Google Scholar
  2. 2.
    K. G. Valeev and O. A. Zhautykov, Infinite Systems of Differential Equations [in Russian], Nauka, Alma-Ata (1974).Google Scholar
  3. 3.
    Yu. L. Daletskii and M. G. Krein, Stability of Differential Equations in Banach Space, American Mathematical Society, Providence, RI (1974).Google Scholar
  4. 4.
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Dover, New York (1999).zbMATHGoogle Scholar
  5. 5.
    A. V. Kostin and S. A. Shchegolev, “On the stability of oscillations representable by Fourier series with slowly varying parameters,” Differents. Uravn., 44, No. 1, 45–51 (2008); English translation: Differ. Equat., 44, No. 1, 47–53 (2008).Google Scholar
  6. 6.
    J. L. Massera and J. J. Schäffer, Linear Differential Equations and Function Spaces, Academic, New York (1966).zbMATHGoogle Scholar
  7. 7.
    A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Kiev (1993).zbMATHGoogle Scholar
  8. 8.
    S. A. Shchegolev, “On one version of the theorem on complete decomposition of a linear homogeneous system of differential equations,” in: Boundary-Value Problems for Differential Equations, Issue 4, Institute of Mathematics, Kyiv (1999), pp. 213–220.Google Scholar
  9. 9.
    M. Almanassra and I. Suwan, “The explicit solution to the countable system of linear ordinary differential equations with constant coefficients,” Mathematica Æterna, 4, No. 8, 827–837 (2014).Google Scholar
  10. 10.
    J. Banaś and M. Lecko, “Solvability of infinite systems of differential equations in Banach sequence spaces,” J. Comput. Appl. Math., 137, No. 2, 363–375 (2001).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • S. A. Shchogolev
    • 1
  • V. V. Jashitova
    • 1
  1. 1.Mechnikov Odessa National UniversityOdessaUkraine

Personalised recommendations