Geodesic
Formal asymptotic solutions of a class of ordinary differential equations in the neighborhood of a turning point
Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 129-139 
L. Yu. Motylev. Formal asymptotic solutions of a class of ordinary differential equations in the neighborhood of a turning point. Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 129-139. http://geodesic.mathdoc.fr/item/SM_1985_51_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Formal asymptotic solutions are constructed for a class of ordinary differential equations of $n$th order with small parameter that have a turning point. An integral representation is proposed for solutions in a small neighborhood of the turning point. Bibliography: 10 titles.

[1] Maslov V. P., Fedoryuk M. V., Kvaziklassicheskoe priblizhenie dlya uravnenii kvantovoi mekhaniki, Nauka, M., 1976 | MR

[2] Maslov V. P., Operatornye metody, Nauka, M., 1973 | MR

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

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

[5] Kheding Dzh., Vvedenie v metod fazovykh integralov (metod VKB), Mir, M., 1965

[6] Langer R. E., “The asymptotic solutions of ordinary linear differential equations of the second order with special reference to a turning point”, Trans Amer. Math. Soc., 67:3 (1949), 461–490 | DOI | MR | Zbl

[7] Kucherenko V. V., Osipov Yu. V., “Asimptoticheskie resheniya giperbolicheskogo uravneniya s kharakteristikami peremennoi kratnosti”, DAN SSSR, 249:2 (1979), 289–293 | MR | Zbl

[8] Olver F., Vvedenie v asimptoticheskie metody i spetsialnye funktsii, Nauka, M., 1978 | MR

[9] Schäfke R., Schmidt D., “The connection problem for general linear ordinary differential equations at two regular singular points with applications in the theory of special functions”, SIAM J. Math. Anal., 11:5 (1980), 848–862 | DOI | MR | Zbl

[10] Schäfke R., “The connection problem for two neighboring regular singular points of general linear complex ordinary differential equations”, SIAM J. Math. Anal., 11:5 (1980), 863–875 | DOI | MR | Zbl