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On an extension theorem and its application for turning point problems of large order. (English) Zbl 0275.34060

MSC:
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34E05 Asymptotic expansions of solutions to ordinary differential equations
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[1] COLE, J. D., Perturbation methods in applied mathematics. Blaisdell Pub. (1968). · Zbl 0162.12602
[2] EVGRAFOV, M. A., AND M. B. FEDORYUK, Asymptotic behavior of solutions o w”(z)–p(z))w(z)=?as -+oo in the complex plane. Uspehi Mat. Nauk 21 (1966), 3-50. · Zbl 0173.33801
[3] FROMAN, M., AND P. O. FROMAN, /KS-approximation. North Holland, Amsterdo (1965).
[4] IWANO, M., AND Y. SIBUYA, Reductions of the order of a linear ordinary differen tial equation containing a small parameter. Kdai Math. Sem. Rep. 15 (1963), 1-28. · Zbl 0115.07001 · doi:10.2996/kmj/1138844728
[5] NAKANO, M., AND T. NISHIMOTO, On a secondary turning point problem. Kda Math. Sem. Rep. 22 (1970), 355-384. · Zbl 0208.11101 · doi:10.2996/kmj/1138846172
[6] NISHIMOTO, T., On matching methods in turning point problems. Kdai Math Sem. Rep. 17 (1965), 198-221. · Zbl 0142.34404 · doi:10.2996/kmj/1138845081
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[8] NISHIMOTO, T., On an extension theorem for turning point problem. Proc. Japa Acad. 47 (1971), 998-1003. · Zbl 0278.34050 · doi:10.3792/pja/1195526314
[9] OLVER, F. W. J., Error analysis of phase-integral methods, I II. J. Res. Nat. Bur Standard Sect. B 69B (1965), 271-290; ibid., 291-300. · Zbl 0138.32401
[10] VAN DYKE, M. D., Perturbation method in fluid mechanics. Academic Press (1964) · Zbl 0136.45001
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[12] WASOW, W., A turning point problem for a system of two linear differentia equations. J. Math. Phys. 38 (1959), 257-278. · Zbl 0091.26003
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