Existence of the boundary in the Chesaro sense of a limited solution of the evolution equation in the Banach space
An existence criterion for the Cesàro limit $\Bigl(\lim_{t \to \infty} \frac{1}{t}\int_{0}^{t} y(\xi) {\rm d}\xi \Bigr)$  of a bounded solution $y(t)$ of the problem ${\rm d}y (t)/{\rm d}t = Ay (t)$, $y(0) = y_0$, $t\in [0, \infty)$, where $А$  is a closed linear operator w...
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| Datum: | 1992 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8181 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | An existence criterion for the Cesàro limit $\Bigl(\lim_{t \to \infty} \frac{1}{t}\int_{0}^{t} y(\xi) {\rm d}\xi \Bigr)$  of a bounded solution $y(t)$ of the problem ${\rm d}y (t)/{\rm d}t = Ay (t)$, $y(0) = y_0$, $t\in [0, \infty)$, where $А$  is a closed linear operator with dense domain of definition $D (A)$ in a reflexive Banach space $E$, is obtained under the condition that there exists a sufficiently small interval $(0, \delta)$ belonging to the set of the regular points $\rho(А)$ of the operator $A$. |
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