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 nonnegative 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.
Keywords:
linear differential equation; spectrum of the upper Sergeev frequencies of zeros; spectrum of the upper Sergeev frequencies of signs; spectrum of the upper Sergeev frequencies of roots; Suslin set.
The work was performed with financial support from the Belarusian Republican Foundation for
Fundamental Research (agreement No. Ф17-102).
Document Type:
Article
UDC:517.926.4
Language: Russian
Citation:
A. S. Vaidzelevich, “On spectra of upper Sergeev frequencies of linear differential equations”, Journal of the Belarusian State University. Mathematics and Informatics, 1 (2019), 28–32
\Bibitem{Vai19}
\by A.~S.~Vaidzelevich
\paper On spectra of upper Sergeev frequencies of linear differential equations
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2019
\vol 1
\pages 28--32
\mathnet{http://mi.mathnet.ru/bgumi71}
\crossref{https://doi.org/10.33581/2520-6508-2019-1-28-32}
Linking options:
https://www.mathnet.ru/eng/bgumi71
https://www.mathnet.ru/eng/bgumi/v1/p28
This publication is cited in the following 8 articles:
A. Kh. Stash, “On Infinite Spectra of Oscillation Exponents of Third-Order Linear Differential Equations”, Russ Math., 68:4 (2024), 42
A. Kh. Stash, “On Some Properties of Strong Oscillation Exponents of Solutions to Homogeneous Linear Differential Equations”, Sib Math J, 65:6 (2024), 1475
A. Kh. Stash, “O kontinualnykh spektrakh pokazatelei koleblemosti lineinykh odnorodnykh differentsialnykh sistem”, Vestnik rossiiskikh universitetov. Matematika, 28:141 (2023), 60–67
A. Kh. Stash, N. A. Loboda, “K voprosu ob ostatochnosti silnykh pokazatelei koleblemosti na mnozhestve reshenii differentsialnykh uravnenii tretego poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:3 (2023), 348–356
A. Kh. Stash, “On Essential Values of Oscillation Exponents for Solutions of a Linear Homogeneous Two-Dimensional Differential System”, Proc. Steklov Inst. Math. (Suppl.), 321:1 (2023), S216–S229
A. Kh. Stash, “On the Control of the Spectra of Upper Strong Oscillation Exponents of Signs, Zeros, and Roots of Third-Order Differential Equations”, Diff Equat, 59:5 (2023), 597
Citation in format AMSBIB
Contact us: