Geodesic
Two problems in the Galois theory of differential fields for the field of formal power series
Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 327-335 
N. V. Grigorenko. Two problems in the Galois theory of differential fields for the field of formal power series. Sbornik. Mathematics, Tome 37 (1980) no. 3, pp. 327-335. http://geodesic.mathdoc.fr/item/SM_1980_37_3_a1/
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     title = {Two problems in the {Galois} theory of differential fields for the field of formal power series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The direct problem in the Galois theory of differential fields for a homogeneous linear differential equation of the second order over the field $\mathbf C((X))$ is solved, and a classification of $SL(2)$-extensions and a description of the Picard–Vessiot extensions of this field are given. Bibliography: 5 titles.

[1] N. V. Grigorenko, “O $G$-primitivnykh rasshireniyakh differentsialnykh polei”, Matem. zametki, 23:3 (1978), 425–434 | MR | Zbl

[2] Zh.-P. Serr, Algebraicheskie gruppy i polya klassov, izd-vo “Mir”, Moskva, 1968

[3] E. R. Kolchin, Differential algebra and algebraic groups, Academic Press, New York, 1973 | MR | Zbl

[4] J. Kovacic, “The invers problem in the Galois theory of differential fields”, Ann. Math., 89 (1969), 583–608 | DOI | MR | Zbl

[5] F. I. Cope, “Formal solutions of irregular linear differential equations”, Amer. J. Math., 58 (1936), 130–140 | DOI | MR | Zbl