Conditions of existence of bounded solutions of differential equation in Banach space on the real axis
Abstract
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.
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Published
2016-05-16
How to Cite
Gorbachuk, V. M. (2016). Conditions of existence of bounded solutions of differential equation in Banach space on the real axis. Transactions of Institute of Mathematics, the NAS of Ukraine, 13(1), 88–97. Retrieved from https://trim.imath.kiev.ua/index.php/trim/article/view/209
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Research papers