Advertisement

Journal of Mathematical Sciences

, Volume 210, Issue 3, pp 270–280 | Cite as

Spectra of Total and Vector Frequencies of Third-Order Linear Differential Equations

  • A. Kh. Stash
Article
  • 17 Downloads

Abstract

For any positive integer N, we construct a linear third-order differential equation with periodic coefficients whose nontrivial solutions have at least N different total (vector) frequencies. Moreover, we construct a linear third-order differential equation with bounded variable coefficients whose nontrivial solutions have countably many total (vector) frequencies.

Keywords

Nontrivial Solution Small Interval Total Frequency Fundamental System Adjacent Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    I. N. Sergeev, “Definition and properties of characteristic frequencies of a linear equation,” Tr. Semin. Petrovskogo, 25, 249–294 (2006).MathSciNetGoogle Scholar
  2. 2.
    I. N. Sergeev, “Properties of the characteristic frequencies of linear equations of arbitrary order,” Tr. Semin. Petrovskogo, 29, 414–442 (2013).Google Scholar
  3. 3.
    I. N. Sergeev, “Definition of total frequencies of solutions of a linear equation,” Differ. Uravn., 44, No. 11, 1577 (2008).MathSciNetGoogle Scholar
  4. 4.
    D. S. Burlakov and S. V. Tsoi, “Coincidence of total and vector frequencies of solutions of linear autonomous systems,” Differ. Uravn., 47, No. 11, 1662–1663 (2011).Google Scholar
  5. 5.
    A. Kh. Stash, “Spectra of total and vector frequencies of third-order linear differential equations,” Differ. Uravn., 48, No. 6, 908 (2012).Google Scholar
  6. 6.
    A. Kh. Stash, “On the set of values of total frequencies of solutions of a linear equation,” Differ. Uravn., 47, No. 11, 1665 (2011).Google Scholar
  7. 7.
    I. N. Sergeev, “Control of solutions of a linear differential equation,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 25–33 (2009).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Adygeya State UniversityMaikopRussia

Personalised recommendations