  The present paper is concerned with strong stability of solutions of
non-autonomous equations of the form $\dot u(t)=A(t)u(t)$, where $A(t)$ is an
unbounded operator in a Banach space depending almost periodically on $t$. A
general condition on strong stability is given in terms of Perron conditions on
the solvability of the associated inhomogeneous equation.

Dynamical Systems;Classical Analysis and ODEs;Functional Analysis;Spectral Theory