On the correct solvability of the Dirichlet problem for operator differential equations in a Banach space

• Date: 2006
• Main Authors: Gorbachuk, V. M., Gorbachuk, M. L., Горбачук, В. М., Горбачук, М. Л.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3547
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the structure of solutions of an equation $y″(t) = By(t)$, where $B$ is a weakly positive operator in a Banach space B, on the interval $(0, \infty)$ and establish the existence of their limit values as $t → 0$ in a broader locally convex space containing $B$ as a dense set. The analy...