Аннотация
Stability problems for solutions of the differential equation u′(t) = Au+ϵB(t, u) in a Banach space are considered. It is assumed that for ϵ = 0 this equation generates a uniformly bounded group of class C0. Sufficient conditions on B and A are found under which the solutions of this equation are bounded for small ϵ. A linearization principle is proved for this equation under certain conditions on the operator B.
Язык оригинала | английский |
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Страницы (с-по) | 1246-1259 |
Число страниц | 14 |
Журнал | Sbornik Mathematics |
Том | 208 |
Номер выпуска | 8 |
DOI | |
Состояние | Опубликовано - 1 янв 2017 |