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On the spectra of oscillation indices of a two-dimensional nonlinear system and its first approximation systemстатья
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Дата последнего поиска статьи во внешних источниках: 23 января 2026 г.
- Автор: Stash A.Kh
- Журнал: Differential Equations
- Том: 61
- Номер: 2
- Год издания: 2025
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 198
- Последняя страница: 210
- DOI: 10.1134/S0012266125020065
- Аннотация: The sets of values (spectra) of the oscillation indices of strict signs, nonstrict signs,zeros, roots, and hyperroots of solutions of differential systems are studied. Two-dimensionalnonlinear systems are constructed all of whose solutions are infinitely extendable to the rightand any of the spectra of their oscillation indices can coincide with the interval[0,1]as wellas with any prescribed nonempty subset of rational numbers of this interval, while the spectraof the linear first approximation systems consist of only one element. Moreover, the spectra ofindices of the original system coincide with the corresponding spectra of oscillation indices of therestriction of the constructed nonlinear two-dimensional systems to the direct product of anyopen neighborhood of zero of the phase plane by the time half-line. In addition, the existence ofa nonlinear system is proved for which the spectrum of any of the oscillation indices in questioncoincides with an arbitrary prescribed subinterval of[0,1], while the corresponding spectra ofthe first approximation system consist of one nonnegative number.
- Добавил в систему: Сташ Айдамир Хазретович