Existence of the boundary in the Chesaro sense of a limited solution of the evolution equation in the Banach space

• Date: 1992
• Main Authors: Gorbachuk , O. L., Yakonska , N. O., Горбачук , О. Л., Яконська , Н. О.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8181
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...