Geodesic
Investigation of the Green's function for differential operators with almost periodic coefficients
Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1027-1054

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The article investigates general properties of linear differential operators of first and second order with almost periodic matrix coefficients in the space of almost periodic vector functions. Conditions for the existence of the Green's function are examined as well as conditions for positivity and negativity of the Green's function relative to certain cones in the phase space. 
@article{IM2_1969_3_5_a5,
     author = {V. Sh. Burd and Yu. S. Kolesov and M. A. Krasnosel'skii},
     title = {Investigation of the {Green's} function for differential operators with almost periodic coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {1027--1054},
     publisher = {mathdoc},
     volume = {3},
     number = {5},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a5/}
}
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V. Sh. Burd; Yu. S. Kolesov; M. A. Krasnosel'skii. Investigation of the Green's function for differential operators with almost periodic coefficients. Izvestiya. Mathematics , Tome 3 (1969) no. 5, pp. 1027-1054. http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a5/