Geodesic
Consistent solutions of linear equations in variational derivatives
Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 176-187

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In this paper, we consider the classical existence problem for consistent and uniformly consistent solutions of linear equations in variational derivatives. In particular, we generalize several results obtained by V. V. Zhikov and B. A. Shcherbakov concerning the existence of almost-periodic, consistent, and uniformly consistent solutions of ordinary differential equations. 
@article{MZM_2005_77_2_a1,
     author = {A. I. Gerko},
     title = {Consistent solutions of linear equations in variational derivatives},
     journal = {Matemati\v{c}eskie zametki},
     pages = {176--187},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a1/}
}
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A. I. Gerko. Consistent solutions of linear equations in variational derivatives. Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 176-187. http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a1/