Geodesic
Investigation of the Green's function for differential operators with almost periodic coefficients
Izvestiya. Mathematics, Tome 3 (1969) no. 5, pp. 1027-1054 
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/
@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},
     year = {1969},
     volume = {3},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a5/}
}
TY  - JOUR
AU  - V. Sh. Burd
AU  - Yu. S. Kolesov
AU  - M. A. Krasnosel'skii
TI  - Investigation of the Green's function for differential operators with almost periodic coefficients
JO  - Izvestiya. Mathematics
PY  - 1969
SP  - 1027
EP  - 1054
VL  - 3
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a5/
LA  - en
ID  - IM2_1969_3_5_a5
ER  - 
%0 Journal Article
%A V. Sh. Burd
%A Yu. S. Kolesov
%A M. A. Krasnosel'skii
%T Investigation of the Green's function for differential operators with almost periodic coefficients
%J Izvestiya. Mathematics
%D 1969
%P 1027-1054
%V 3
%N 5
%U http://geodesic.mathdoc.fr/item/IM2_1969_3_5_a5/
%G en
%F IM2_1969_3_5_a5

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

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.

[1] Gantmakher F. R., Teoriya matrits, Fizmatgiz, M., 1967

[2] Zabreiko P. P., Krasnoselskii M. A., Stetsenko V. Ya., “Ob otsenkakh spektralnogo radiusa lineinykh polozhitelnykh operatorov”, Matemat. zametki, 1:4 (1967), 461–468 | MR | Zbl

[3] Kolesov Yu. S., Polozhitelnye periodicheskie resheniya sistem obyknovennykh differentsialnykh uravnenii, Dissertatsiya, Voronezh, 1966 | Zbl

[4] Krasnoselskii M. A., Polozhitelnye resheniya operatornykh uravnenii, Fizmatgiz, M., 1962 | MR

[5] Krein M. G., Rutman M. A., “Lineinye operatory, ostavlyayuschie invariantnym konus v prostranstve Banakha”, Uspekhi matem. nauk, 3:1(23) (1948), 3–95 | MR | Zbl

[6] Levitan B. M., Pochti periodicheskie funktsii, Gostekhizdat, M., 1952

[7] Massera J. L., Schäffer I. I., Linear differential equations and function spaces, Acad. Press, N. Y., 1966 | MR | Zbl

[8] Massera J. L., Schäffer I. I., “Linear differential equations and functional analysis. I”, Ann. Math., 67:3 (1958), 517–573 | DOI | MR | Zbl