Abstract
A study is made of the linear equation pt′ = A(t) p +f(t) with an almost periodic matrix A(t) and an almost periodic free termf(t). It is shown that if a bounded solution exists, then an almost periodic solution in the sense of Besicovitch also exists.
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B. M. Levitan, Almost Periodic Functions [in Russian], Moscow (1953).
H. Bohr and O. Neugebauer, “Über lineare Differentialgleichungen mit konstanten Koeffizienten und fastperiodischer Rechter,” Gött. Nachr., 8–22 (1926).
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V. V. Zhikov, “On the problem of the existence of almost periodic solutions of differential and operator equations,” Compendium of papers of the Vladimir Polytechnical Institute [in Russian], 94–188 (1969).
V. V. Zhikov, “On criteria of almost periodicity,” Compendium of papers on the “Theory of Functions and Its Applications” [in Russian], No. 4, 171–175, Khar'kov (1967).
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Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 239–246, February, 1970.
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Zhikov, V.V. Addition to the classical theory of Favard. Mathematical Notes of the Academy of Sciences of the USSR 7, 142–146 (1970). https://doi.org/10.1007/BF01093499
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DOI: https://doi.org/10.1007/BF01093499