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On some properties of strong oscillation exponents of solutions to homogeneous linear differential equationsстатья
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Дата последнего поиска статьи во внешних источниках: 23 января 2026 г.
- Автор: Stash A.Kh
- Журнал: Siberian Mathematical Journal
- Том: 65
- Номер: 6
- Год издания: 2024
- Издательство: Maik Nauka/Interperiodica Publishing
- Местоположение издательства: Russian Federation
- Первая страница: 1475
- Последняя страница: 1482
- DOI: 10.1134/S0037446624060235
- Аннотация: Within the theory of Lyapunov exponents and the oscillation theory, we study varioustypes of oscillation exponents (upper or lower, strong or weak) of strict signs, nonstrict signs, zeros,roots, and hyperroots of nonzero solutions to homogeneous linear differential equations with continuouscoefficients on the positive semiaxis. We construct some example of a homogeneous linear differentialequation of order greater than 2 whose spectra of the upper strong oscillation exponents of strictsigns, zeros and roots coincide with a given Suslin set of the nonnegative semiaxis of the extended realaxis which contains zero. At the same time, all listed oscillation exponents are absolute on the setof solutions of the equation. We use the analytical methods of the qualitative theory of differentialequations, in particular, the author’s technique for controlling the fundamental system of solutions tothese equations in one particular case. We then prove that the strong oscillation exponents of nonstrictsigns, zeros, roots, and hyperroots are not residual on the set of solutions of equations of order greaterthan 2. As a consequence, we demonstrate the existence of a function from the set with the followingproperties: All listed oscillation exponents are accurate, but not absolute. In this event, all strongexponent as well as weak exponents are equal to each other.
- Добавил в систему: Сташ Айдамир Хазретович