Construction of asymptotic fundamental systems for linear differential equations with transition points

Hans-Görg Roos

Commentationes Mathematicae Universitatis Carolinae (1979)

  • Volume: 020, Issue: 2, page 195-205
  • ISSN: 0010-2628

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Roos, Hans-Görg. "Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten." Commentationes Mathematicae Universitatis Carolinae 020.2 (1979): 195-205. <http://eudml.org/doc/16964>.

@article{Roos1979,
author = {Roos, Hans-Görg},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear differential equations; turning point; singular perturbations},
language = {ger},
number = {2},
pages = {195-205},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten},
url = {http://eudml.org/doc/16964},
volume = {020},
year = {1979},
}

TY - JOUR
AU - Roos, Hans-Görg
TI - Die Konstruktion asymptotischer Fundamentalsysteme für lineare Differentialgleichungen mit Wendepunkten
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1979
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 020
IS - 2
SP - 195
EP - 205
LA - ger
KW - linear differential equations; turning point; singular perturbations
UR - http://eudml.org/doc/16964
ER -

References

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  1. ANYANWU D. U., Uniform asymptotic solution of nonhomogeneous differential equations with turning points, SIAM J. Math. Anal. 8 (1977), 710-718. (1977) MR0596985
  2. ANYANWU D. U., KELLER J. B., A solution of higher order differential equations with several turning points, Comm. pure appl. Math. 31 (1978), 107-121. (1978) MR0486874
  3. BAKKEN I., On the central connection problem for a class of ordinary differential equations, Funkcial. Ekvac. 20 (1977), 115-156. (1977) MR0499531
  4. BRAAKSMA B. L. J., Recessive solutions of linear differential equations with polynomial coefficients, Lecture Notes Math. 280 (1972), 1-15. (1972) Zbl0242.34007MR0477226
  5. EВГРАФОВ M. A., ФЕДОРЮК M. B., Accимптотикаa peшений W * - p ( x , λ ) w = 0 npи X в комплексной плоскости z , Успехи матем. наук 21 (1966), 3-50. (1966) 
  6. GROEN P. P. N., Singular perturbed differential operators of second order, Amsterdam 1976. (1976) 
  7. IWANO M., SIBUYA A., Reduction of the order of linear ordinary differential equation containing a small parameter, Kodai math. sem. rep. 15 (1963), 1-23. (1963) MR0149034
  8. JURKAT W. B., Meromorphe Differentialgleichungen, Lecture Notes Math. 637 (1978). (1978) Zbl0408.34004MR0494886
  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. (1969) MR0245919
  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). (1973) Zbl0252.34063MR0333382
  11. LEUNG A., Lateral connections for asymptotic solutions around higher order turning points, J. Math. Anal. Appl. 50 (1975), 560-578. (1975) Zbl0303.34044MR0372356
  12. LEUNG A., Doubly asymptotic series for n -th order differential equations, SIAM J. Math. Anal. 5 (1974), 187-201. (1974) Zbl0289.34081MR0348209
  13. LEUNG A., A dubly asymptotic existence theorem and application to order reduction, Proc. London Math. Soc. 33 (1976), 151-176. (1976) MR0412543
  14. LEUNG A., A third-order linear differential equation on the real line with two turning points, J. diff. equ. 29 (1978), 304-328. (1978) Zbl0397.34075MR0492643
  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. (1970) Zbl0194.12202MR0261100
  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. (1971) MR1554147
  17. NAKAKO M., NISHIMOTO T., On a secondary turning point problem, Kodai Math. Sem. Rep. 22 (1970), 365-384. (1970) MR0265696
  18. NISHIMOTO T., On matching methods in turning point problems, Kodai Math. Sem. Rep. 17 (1965), 198-221. (1965) Zbl0142.34404MR0183945
  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. (1965) 
  20. NISHIMOTO T., On the central connection problem at a turning point, Kodai Math. Sem. Rep. 22 (1970), 30-44. (1970) Zbl0193.05202MR0265696
  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. (1973) Zbl0275.34060MR0335986
  22. NISHIMOTO T., Asymptotic behaviour of the WKB approximations near a Stokes curve, Kodai Math. Sem. Rep. 29 (1977), 71-87. (1977) MR0486877
  23. OLVER F., Asymptotic and special functions, Academic press, New York 1974. (1974) 
  24. OLVER F., Connection formulas for second order differential equations with multiple turning points, SIAM J. Math. Anal. 8 (1977), 127-154. (1977) Zbl0344.34050MR0427763
  25. OLVER F., Connection formulas for second order differential equations having an arbitrary number of turning points of arbitrary multiplicites, SIAM J. Math. Anal. 8 (1977), 673-700. (1977) MR0454215
  26. OLVER F., Sufficient conditions for Ackerberg-O'Malley resonance, SIAM J. Math. Anal. 9 (1978), 328-355. (1978) Zbl0375.34034MR0470383
  27. ROOS H.-G., Die asymptotische Lösung einer linearen Differentialgleichung zweiter Qrdnung mit zweisegmentigen charakteristischen Polygon, Beiträge zur Analysis 7 (1975), 55-63. (1975) MR0470384
  28. ROOS H.-G., Die Konstruktion eines asymptotischen Fundamentalsystems für eine lineare Differentialgleichung vom hydrodynamischen Typ, ZAMM 56 (1976), 401-408. (1976) Zbl0337.34054MR0431925
  29. ROOS H.-G., Die asymptotische Lösung einer linearen Differentialgleichung mit dreisegmentigem charaktetistischen Polygon, Mathematische Nachrichten (im Druck). 
  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. (1977) MR0437869
  31. SIBUYA Y., Uniform simplification in a full neighborhood of a transition point, Mem. Amer. Math. Soc. no 149 (1974). (1974) Zbl0297.34051MR0440140
  32. SIBUYA Y., Global theory of second order linear ordinary differential equations with a polynomial coefficient, North Holland Math. Studies 18, Amsterdam 1975. (1975) 
  33. WASOW W., Asymptotic expansions fee ordinary differential equations, Interscience, New York 1965. (1965) 
  34. WASOW W., The central connection problem at turning points of linear differential equations, Comment. Math. Helv. 46 (1971), 65-86. (1971) Zbl0218.34010MR0285775
  35. WASOW W., Simple turning-point problems in unbounded domains, SIAM J. Math. Anal. 1 (1970), 153-170. (1970) Zbl0211.11002MR0259259
  36. WILLNER B., RUBENFELD L., Uniform asymptotic solution for a linear ordinary differential equation with one μ -th order turning point, Comm. Pure Appl. Math. 29 (1976), 343-367. (1976) MR0425282
  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. (1977) MR0440141

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