Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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On the Discontinuity of Extreme Exponents of Oscillation on a Set of Linear Homogeneous Differential Systems

Author(s):

Aydamir Khazretovich Stash

Adyghe State University, Dean of the Faculty of Mathematics and Computer Science

aidamir.stash@gmail.com

Abstract:

In this paper, we study the questions of the discontinuity of the extreme oscillation exponents on the set of linear homogeneous differential systems with continuous coefficients on the positive axis. The existence of points on a set of differential systems is established in which all the higher and lower exponents of the oscillation zeros, roots, and hypercorns are not only not continuous, but are not continuous either from above or from below. Moreover, the non-invariance of the extreme exponent of oscillations with respect to infinitesimal perturbations has been proved. When proving the results of this work, the cases of parity and odd order of the matrix of the system are considered separately.

Keywords

References:

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