Geodesic
The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory)
Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 409-414

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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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     author = {V. V. Zhikov},
     title = {The existence of {Levitan} almost-periodic solutions of linear systems (second complement to {Favard's} classical theory)},
     journal = {Matemati\v{c}eskie zametki},
     pages = {409--414},
     publisher = {mathdoc},
     volume = {9},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a5/}
}
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V. V. Zhikov. The existence of Levitan almost-periodic solutions of linear systems (second complement to Favard's classical theory). Matematičeskie zametki, Tome 9 (1971) no. 4, pp. 409-414. http://geodesic.mathdoc.fr/item/MZM_1971_9_4_a5/