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Zbl 0749.34035
Xiao, Tijun; Liang, Jin
Second order linear differential equations with almost periodic solutions.
(English)
[J] Acta Math. Sin., New Ser. 7, No.4, 354-359 (1991). ISSN 1000-9574; ISSN 1439-7617/e

Let $A$ be the infinitesimal generator of a strongly continuous cosine function $C(t)$. A characterization of those $A$ for which $C(t)$ is almost periodic is known: the authors characterize the operators $A$ for which the sine function $S(t)u=\int\sp t\sb 0C(s)uds$ is almost periodic.
[H.O.Fattorini (Los Angeles)]
MSC 2000:
*34G10 Linear ODE in abstract spaces
34C27 Almost periodic solutions of ODE

Keywords: linear differential equations in abstract spaces; infinitesimal generator; almost periodic; operators

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