Asymptotic Behavior of Linear Almost Periodic Differential Equations
  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. 
Bui Xuan Dieu, Luu Hoang Duc, Stefan Siegmund, Nguyen Van Minh
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