Almost-periodic solutions of differential-operator equations (Q788173)

In the paper is proposed a simple method which enables to obtain sufficient conditions for the existence of various classes of almost- periodic solutions of the equations of the type \(P(d/dt)u=\sum^{m}_{k=0}A_ kd^ ku/dt^ k=f,\) \(t\in {\mathbb{R}}\), where \(A_ k\in L(D,X)\) and f is an almost periodic function with values in the Banach space X. Here L(D,X) is the space of bounded linear operators from D into X, where D and X are complex Banach spaces.