Geodesic
Addition to the classical theory of Favard
Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 239-246

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A study is made of the linear equation $p'(t)=A(t)p+f(t)$ with an almost periodic matrix $A(t)$ and an almost periodic free term $f(t)$. It is shown that if a bounded solution exists, then an almost periodic solution in the sense of Besicovitch also exists. 
@article{MZM_1970_7_2_a12,
     author = {V. V. Zhikov},
     title = {Addition to the classical theory of {Favard}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {239--246},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a12/}
}
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V. V. Zhikov. Addition to the classical theory of Favard. Matematičeskie zametki, Tome 7 (1970) no. 2, pp. 239-246. http://geodesic.mathdoc.fr/item/MZM_1970_7_2_a12/