| Title:
|
Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten (German) |
| Title:
|
Construction of asymptotic fundamental systems for linear differential equations with transition points (English) |
| Author:
|
Roos, Hans-Georg |
| Language:
|
German |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
20 |
| Issue:
|
2 |
| Year:
|
1979 |
| Pages:
|
195-205 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34E20 |
| idZBL:
|
Zbl 0418.34012 |
| idMR:
|
MR539551 |
| . |
| Date available:
|
2008-06-05T21:01:13Z |
| Last updated:
|
2012-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/105921 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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[8] JURKAT W. B.: Meromorphe Differentialgleichungen.Lecture Notes Math. 637 (1978). Zbl 0408.34004, MR 0494886 |
| Reference:
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[9] LEE R.: On the uniform simplification of linear differential equations in a full neighborhood of a turning point.J. Math. Anal. Appl. 27 (1969), 601-510. MR 0245919 |
| Reference:
|
[10] LEUNG A.: Connection formulas for asymptotic solutions of second order turning points in unbounded domains.SIAM J. Math. Anal. 4 (1973), 89-103 (Errata: 6 (1975), 600). Zbl 0252.34063, MR 0333382 |
| Reference:
|
[11] LEUNG A.: Lateral connections for asymptotic solutions around higher order turning points.J. Math. Anal. Appl. 50 (1975), 560-578. Zbl 0303.34044, MR 0372356 |
| Reference:
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[12] LEUNG A.: Doubly asymptotic series for $n$-th order differential equations.SIAM J. Math. Anal. 5 (1974), 187-201. Zbl 0289.34081, MR 0348209 |
| Reference:
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[13] LEUNG A.: A dubly asymptotic existence theorem and application to order reduction.Proc. London Math. Soc. 33 (1976), 151-176. MR 0412543 |
| Reference:
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[14] LEUNG A.: A third-order linear differential equation on the real line with two turning points.J. diff. equ. 29 (1978), 304-328. Zbl 0397.34075, MR 0492643 |
| Reference:
|
[15] LYNN R., KELLER J.: Uniform asymptotic solutions of second order linear ordinary differential equations with turning points.Comm. Pure Appl. Math, 23 (1970), 379-408. Zbl 0194.12202, MR 0261100 |
| Reference:
|
[16] MC HUGH J.: A historical survey of ordinary linear differential equations with a large parameter and turning points.Arch. History Exact. Sci. 7 (1971), 277-324. MR 1554147 |
| Reference:
|
[17] NAKAKO M., NISHIMOTO T.: On a secondary turning point problem.Kodai Math. Sem. Rep. 22 (1970), 365-384. MR 0265696 |
| Reference:
|
[18] NISHIMOTO T.: On matching methods in turning point problems.Kodai Math. Sem. Rep. 17 (1965), 198-221. Zbl 0142.34404, MR 0183945 |
| Reference:
|
[19] NISHIMOTO T.: On a matching method for a linear ordinary differential equation containing a small parameter.Kodai Math. Sem. Rep. 17 (1965), 307-328, 18 (1966), 61-86, 19 (1967), 80-94. |
| Reference:
|
[20] NISHIMOTO T.: On the central connection problem at a turning point.Kodai Math. Sem. Rep. 22 (1970), 30-44. Zbl 0193.05202, MR 0265696 |
| Reference:
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[21] NISHIMOTO T.: On an extension theorem and its application for turning point problems of large order.Kodai Math. Sem. Rep. 25 (1973), 458-489. Zbl 0275.34060, MR 0335986 |
| Reference:
|
[22] NISHIMOTO T.: Asymptotic behaviour of the WKB approximations near a Stokes curve.Kodai Math. Sem. Rep. 29 (1977), 71-87. MR 0486877 |
| Reference:
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[23] OLVER F.: Asymptotic and special functions.Academic press, New York 1974. |
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[26] OLVER F.: Sufficient conditions for Ackerberg-O'Malley resonance.SIAM J. Math. Anal. 9 (1978), 328-355. Zbl 0375.34034, MR 0470383 |
| Reference:
|
[27] ROOS H.-G.: Die asymptotische Lösung einer linearen Differentialgleichung zweiter Qrdnung mit zweisegmentigen charakteristischen Polygon.Beiträge zur Analysis 7 (1975), 55-63. MR 0470384 |
| Reference:
|
[28] ROOS H.-G.: Die Konstruktion eines asymptotischen Fundamentalsystems für eine lineare Differentialgleichung vom hydrodynamischen Typ.ZAMM 56 (1976), 401-408. Zbl 0337.34054, MR 0431925 |
| Reference:
|
[29] ROOS H.-G.: Die asymptotische Lösung einer linearen Differentialgleichung mit dreisegmentigem charaktetistischen Polygon.Mathematische Nachrichten (im Druck). |
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[30] RUBENFELD L., WILLNER B.: Uniform asymptotic solution for linear second order ordinary differential equations with turning points.SIAM J. Appl. Math. 32 (1977), 21-38. MR 0437869 |
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|
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|
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| Reference:
|
[35] WASOW W.: Simple turning-point problems in unbounded domains.SIAM J. Math. Anal. 1 (1970), 153-170. Zbl 0211.11002, MR 0259259 |
| Reference:
|
[36] WILLNER B., RUBENFELD L.: Uniform asymptotic solution for a linear ordinary differential equation with one $\mu $-th order turning point.Comm. Pure Appl. Math. 29 (1976), 343-367. MR 0425282 |
| Reference:
|
[37] WYRWIGH H.: An explicit solution of the central connection problem for an $n$-th order linear ordinary differential equation with polynomial coefficients.SIAM J. Math. Anal. 8 (1977), 412-422. MR 0440141 |
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