Geodesic
Boundary value problems for systems of ordinary differential equations
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 30 (1987), pp. 3-103 
I. T. Kiguradze. Boundary value problems for systems of ordinary differential equations. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Itogi Nauki i Tekhniki. Seriya "Sovremennye Problemy Matematiki. Noveishie Dostizheniya", Tome 30 (1987), pp. 3-103. http://geodesic.mathdoc.fr/item/INTD_1987_30_a0/
@article{INTD_1987_30_a0,
     author = {I. T. Kiguradze},
     title = {Boundary value problems for systems of ordinary differential equations},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {3--103},
     year = {1987},
     volume = {30},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1987_30_a0/}
}
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This article contains an exposition of fundamental results of the theory of boundary-value problems for systems of linear and nonlinear ordinary differential equations. In particular, criteria are given for problems with functional, many-point, and two-point boundary conditions to be solvable and well-posed, as well as methods of finding approximate solutions. We also examine questions of existence, uniqueness, and stability of periodic and bounded solutions of nonautonomous differential systems.