Second order linear differential equations with almost periodic solutions. (English) Zbl 0749.34035

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 \(S(t)u=\int^ t_ 0C(s)uds\) is almost periodic.


34G10 Linear differential equations in abstract spaces
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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[1] Cioranescu, I., Characterizations of almost periodic strongly continuous cosine operator functions,J. Math. Anal. Appl.,116 (1986), 222–229. · Zbl 0604.47026
[2] Fattorini, H. O., Second order linear differential equations in Banach spaces, Elsevier Science Publishers B. V., Amsterdam, 1985. · Zbl 0564.34063
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