Lizama, Carlos Mild almost periodic solutions of abstract differential equations. (English) Zbl 0698.47035 J. Math. Anal. Appl. 143, No. 2, 560-571 (1989). 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 Cited in 3 Documents MSC: 47E05 General theory of ordinary differential operators 35J10 Schrödinger operator, Schrödinger equation 34G10 Linear differential equations in abstract spaces 35L05 Wave equation Keywords:existence of mild almost periodic solutions of Cauchy problems; infinitesimal generator of a strongly continuous semigroup; Schrödinger equation; wave equation PDFBibTeX XMLCite \textit{C. Lizama}, J. Math. Anal. Appl. 143, No. 2, 560--571 (1989; Zbl 0698.47035) Full Text: DOI References: [1] Amerio, M.; Prouse, G., Almost Periodic Functions and Functional Equations (1971), Van Nostrant-Reinhold: Van Nostrant-Reinhold Princeton, NJ · Zbl 0215.15701 [2] Cioranescu, I.; Lizama, C., Spectral properties of cosine operator functions, Aequationes Math., 36, 80-98 (1988) · Zbl 0675.47029 [3] Corduneanu, C., Almost Periodic Functions (1968), Interscience: Interscience New York · Zbl 0175.09101 [4] Davies, E., One Parameter Semigroups (1980), Academic Press: Academic Press New York/London · Zbl 0457.47030 [5] Fattorini, H., Second Order Linear Differential Equations in Banach Spaces, (North-Holland Mathematics Studies, No. 108 (1985), North-Holland: North-Holland Amsterdam) · Zbl 0564.34063 [6] Foias, C.; Zaidman, S., Almost periodic solutions of parabolic systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 15, 247-262 (1961), (3) · Zbl 0100.30303 [7] Haraux, A., Nonlinear Evolution Equations—Global Behavior of Solutions, (Lecture Notes in Mathematics, Vol. 841 (1981), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0583.35007 [8] Levitan, B.; Zhikov, V., Almost Periodic Functions and Differential Equations (1982), Cambridge Univ. Press: Cambridge Univ. Press London/New York · Zbl 0499.43005 [9] Nagel, N., One Parameter Semigroups of Positive Operators, (Lecture Notes in Mathematics, Vol. 1184 (1986), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0585.47030 [10] Nagy, B., On cosine operator functions in Banach spaces, Acta Sci. Math., 36, 281-289 (1974) · Zbl 0273.47008 [11] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer-Verlag: Springer-Verlag Berlin/New York · Zbl 0516.47023 [12] Pruss, J., On the spectrum of \(C_0\)-semigroups, Trans. Amer. Math. Soc., 284, 847-857 (1984) · Zbl 0572.47030 [13] Zaidman, S., Uniqueness of bounded solutions for some abstract differential equations, Ann. Univ. Ferrara Ser. VII, 14, 101-104 (1969) · Zbl 0218.34059 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.