On spectra of upper Sergeev frequencies of linear differential equations

  • Aliaksei S. Vaidzelevich Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surhanava Street, Minsk 220072, Belarus https://orcid.org/0000-0002-7466-4761

Abstract

It is known that the spectra (ranges) of upper and lower Sergeev frequencies of zeros, signs, and roots of a linear differential equation of order greater than two with continuous coefficients belong to the class of Suslin sets on the nonnegative half-line of the extended real line. Moreover, for the spectra of upper frequencies of third-order equations this result was inverted under the assumption that the spectra contain zero. In the present paper we obtain an inversion of the above statement for equations of the fourth order and higher. Namely, for an arbitrary zero-containing Suslin subset S on the non-negative half-line of the extended real line and a positive integer number n greater than three a n order linear differential equation is constructed, which spectra of the upper Sergeev frequencies of zeros, signs, and roots coincide with the set S.

Author Biography

Aliaksei S. Vaidzelevich, Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surhanava Street, Minsk 220072, Belarus

PhD (physics and mathematics); senior researcher at the department of differential equations

References

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Published
2019-04-08
Keywords: linear differential equation, spectrum of the upper Sergeev frequencies of zeros, spectrum of the upper
Supporting Agencies The work was performed with financial support from the Belarusian Republican Foundation for Fundamental Research (agreement No. Ф17-102).
How to Cite
Vaidzelevich, A. S. (2019). On spectra of upper Sergeev frequencies of linear differential equations. Journal of the Belarusian State University. Mathematics and Informatics, 1, 28-32. https://doi.org/10.33581/2520-6508-2019-1-28-32