Geodesic
Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions
Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 553-560

Voir la notice de l'article provenant de la source Math-Net.Ru

An example is given of a finite-dimensional equation $u'+A(t)u=f(t)$, where $A(t)$ and $f(t)$ are Bohr almost periodic elements, having bounded solutions but not almost periodic solutions (the question of a similar example was already posed and discussed in Favard's original papers). On the other hand, solvability in the Besicovitch class does not require subtle separability or stability conditions. General theorems of such a kind are provided in this note. 
@article{MZM_1975_18_4_a7,
     author = {V. V. Zhikov},
     title = {Solvability of linear equations in the {Besicovitch} and {Bohr} classes of almost periodic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {553--560},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a7/}
}
TY  - JOUR
AU  - V. V. Zhikov
TI  - Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions
JO  - Matematičeskie zametki
PY  - 1975
SP  - 553
EP  - 560
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a7/
LA  - ru
ID  - MZM_1975_18_4_a7
ER  - 
%0 Journal Article
%A V. V. Zhikov
%T Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions
%J Matematičeskie zametki
%D 1975
%P 553-560
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a7/
%G ru
%F MZM_1975_18_4_a7
V. V. Zhikov. Solvability of linear equations in the Besicovitch and Bohr classes of almost periodic functions. Matematičeskie zametki, Tome 18 (1975) no. 4, pp. 553-560. http://geodesic.mathdoc.fr/item/MZM_1975_18_4_a7/