Geodesic
Proof of the Favard theorem on the existence of almost-periodic solution for an arbitrary Banach space
Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 121-126 Cet article a éte moissonné depuis la source Math-Net.Ru

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The well-known Favard-Amerio theorem on the existence of an almost-periodic solution of a linear equation is based on the geometry of a uniformly convex space, since the almost-periodic solution is found by the minimax condition. In the present note an essentially different method for finding the almost-periodic solution is developed, which enables us to prove the Favard-Amerio theorem for an arbitrary Banach space. 
@article{MZM_1978_23_1_a12,
     author = {V. V. Zhikov},
     title = {Proof of the {Favard} theorem on the existence of almost-periodic solution for an arbitrary {Banach} space},
     journal = {Matemati\v{c}eskie zametki},
     pages = {121--126},
     year = {1978},
     volume = {23},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a12/}
}
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V. V. Zhikov. Proof of the Favard theorem on the existence of almost-periodic solution for an arbitrary Banach space. Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 121-126. http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a12/