Conditions of existence of bounded solutions of differential equation in Banach space on the real axis

• Date: 2016
• Author Affiliations: В. М. Горбачук — Нацiональний технiчний унiверситет України "КПI"
• Keywords: keywords
• Main Authors: Gorbachuk, V. M., Горбачук, В. М.
• Format: Article
• Language: Ukrainian
• Published: Інститут математики НАН України 2016
• Online Access: https://trim.imath.kiev.ua/index.php/trim/article/view/209
• Journal Title: Transactions of Institute of Mathematics of NAS of Ukraine

We consider an equation of the form $y''(t)- By(t) = f(t), \ t \in (-\infty, \infty)$, where $B$ is a positive operator in a Banach space. For the vector-valued function $f(t)$, we establish sufficient conditions under which a bounded solution to this equation exists and is unique.