On bounded solutions of differential inclusions in Banach spaces (Q1118087)

The existence and asymptotic properties of bounded solutions of differential inclusions in separable Banach spaces are established. The inclusions have the form \(\dot x(t)\in A(t)x(t)+F(t,x(t)),\) \(t\in {\mathbb{R}}_+\), where F satisfies Carathéodory-type conditions and a regularity condition. The results extend those of Coppel [Mathematical Monographs, Heath (Boston (1965)], \textit{J. L. Massera} and \textit{J. J. Schaffer} [Linear differential equations and function spaces (1966; Zbl 0243.34107)] and \textit{S. Szufla} [Comment. Math. 21, 381-387 (1979; Zbl 0432.34040)].