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Mild almost periodic solutions of abstract differential equations. (English) Zbl 0698.47035

Summary: “Necessary and sufficient conditions are established for the existence of mild almost periodic solutions of Cauchy problems \(u'=Au+f\) and \(u''=Au+f\), where A is the infinitesimal generator of a strongly continuous semigroup (respectively, a cosine function) on a Hilbert space and f an almost periodic function.” There is given an application to the Schrödinger equation and the wave equation.
Reviewer: S.Stanek

MSC:

47E05 General theory of ordinary differential operators
35J10 Schrödinger operator, Schrödinger equation
34G10 Linear differential equations in abstract spaces
35L05 Wave equation
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References:

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