Geodesic
Normal solvability of linear differential equations in the complex plane
Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 445-466

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The operator $L_nY=A(z)Y'(z)+B(z)Y(z)$, where $A(z)$ and $B(z)$ are square $n$th order matrices, regular in a region $G$ of arbitrary connectivity, and $Y(z)$ is a single-column matrix, regular in $G$, is investigated. The operator $L_nY$ is shown to be normally solvable in the space $A^n(G)$ of single-column matrices regular in $G$, and in certain subspaces of $A^n(G)$, and its index is evaluated. 
@article{IM2_1972_6_2_a7,
     author = {Yu. F. Korobeinik},
     title = {Normal solvability of linear differential equations in the complex plane},
     journal = {Izvestiya. Mathematics },
     pages = {445--466},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/}
}
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Yu. F. Korobeinik. Normal solvability of linear differential equations in the complex plane. Izvestiya. Mathematics , Tome 6 (1972) no. 2, pp. 445-466. http://geodesic.mathdoc.fr/item/IM2_1972_6_2_a7/