Abstract
The linear equation u′ = A(t) u +f(t) with almost periodic coefficients is investigated in euclidean space. It is proved that if it has a bounded solution, then it has a Levitan almost-periodic function as a “limit” solution.
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Translated from Matematicheskie Zametki, Vol. 9, No. 4, pp. 409–414, April, 1971.
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Zhikov, V.V. The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory). Mathematical Notes of the Academy of Sciences of the USSR 9, 235–238 (1971). https://doi.org/10.1007/BF01387771
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DOI: https://doi.org/10.1007/BF01387771