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JOURNALS // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika // Archive

Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2023 Number 5, Pages 16–22 (Mi vmumm4563)

Mathematics

Existence of infinite everywhere discontinuous spectra of upper indicators in changes of signs, zeros and roots for third order differential equations

A. Kh. Stash, A. E. Artisevich

Department of Mathematics and Computer Science, Adyghe State University, Maikop

Abstract: Examples of two linear homogeneous differential equations of the third order are constructed, the spectra of the upper strong exponents of oscillation of signs, zeros and roots of one of which coincide with the set of rational numbers of the segment $[0,1]$, and the other with the set of irrational numbers of the segment $[0,1]$ augmented with the number zero.

Key words: differential equations, oscillation, number of zeros, exponents of oscillation, Sergeev frequencies, Lyapunov exponents.

UDC: 517.926

Received: 25.12.2022

DOI: 10.55959/MSU0579-9368-1-64-5-3


 English version:
Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2023, 78:5, 223–229

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© Steklov Math. Inst. of RAS, 2024