Geodesic
Exact and asymptotic solutions of systems with turning points
Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 355-370.

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A system of linear ordinary differential equations with analytic coefficients and small parameters on the derivative is considered. In a neighborhood of a turning point a new representation is constructed for the exact solution of the system in the form of a multiphase series. It is proved that this series converges uniformly with respect to the parameter. An expression is obtained for the Stokes constant at the maximal exponential. Bibligraphy: 10 titles. 
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V. V. Kucherenko; Yu. V. Osipov. Exact and asymptotic solutions of systems with turning points. Izvestiya. Mathematics , Tome 29 (1987) no. 2, pp. 355-370. http://geodesic.mathdoc.fr/item/IM2_1987_29_2_a4/

[1] Kucherenko V. V., “Asimptoticheskie resheniya sistemy $A(x, -ih\partial/\partial x)u=0$ pri $h\to 0$ v sluchae kharakteristik peremennoi kratnosti”, Izv. AN SSSR. Ser. matem., 38:3 (1974), 625–662 | Zbl

[2] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl

[3] Plemelj J., Problems in the sense of Riemann and Klein, Interscience, 1964 | MR | Zbl

[4] Schlesinger L. J., “Über eine Klasse von Differentialsystemen beliebiger Ordnung mit festen kritischen Punkten”, Journ. reine und angew. Mathematik, 141 (1912), 96–145 | Zbl

[5] Maslov V. P., Teoriya vozmuschenii i asimptoticheskie metody, MGU, M., 1965

[6] Kucherenko V. V., Osipov Yu. V., “Asimptoticheskie resheniya obyknovennykh differentsialnykh uravnenii s vyrozhdayuschimsya simvolom”, Matem. sb., 118(160):1 (1982), 74–103 | MR | Zbl

[7] Fedoryuk M. V., Metod perevala, Nauka, M., 1977 | MR

[8] Evgrafov M. A., Fedoryuk M. V., “Asimptotika reshenii uravneniya $w''(z)-p(z,\lambda)\cdot w(z)=0$ pri $\lambda\to\infty$ v kompleksnoi ploskosti $z$”, Uspekhi matem. nauk, 21:1 (1966), 3–50 | MR | Zbl

[9] Vazov V., Asimptoticheskie razlozheniya reshenii differentsialnykh uravnenii, Mir, M., 1968

[10] Shabat B. V., Vvedenie v kompleksnyi analiz, Nauka, M., 1976 | MR