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On the asymptotic solutions of a class of ordinary differential equations of the fourth order, with special reference to an equation of hydrodynamics


Author: Rudolph E. Langer
Journal: Trans. Amer. Math. Soc. 84 (1957), 144-191
MSC: Primary 34.0X
DOI: https://doi.org/10.1090/S0002-9947-1957-0083637-0
MathSciNet review: 0083637
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  • [1] Wolfgang Wasow, A study of the solutions of the differential equation $ {y^{(4)}} + {\lambda ^2}(xy'' + y) = 0$ for large values of $ \lambda $, Ann. of Math. vol. 52 (1950) pp. 350-361. MR 0037432 (12:261b)
  • [2] -, Asymptotic solution of the differential equation of hydrodynamic stability in a domain containing a transition point, Ann. of Math. vol. 58 (1953) pp. 222-252. MR 0061737 (15:874b)
  • [3] -, On small disturbances of plane Couette flow, Journal of Research of the National Bureau of Standards (Washington, D. C.) vol. 51 (1953) pp. 195-202. MR 0059706 (15:573c)
  • [4] D. Meksyn, Fluid motion between parallel planes. Dynamical stability, Proc. Roy. Soc. London Ser. A vol. 186 (1946) pp. 391-409. MR 0017067 (8:105g)
  • [5] -, Asymptotic integrals of a fourth order differential equation containing a large parameter, Proc. London Math. Soc. Ser. 2 vol. 49 (1947) pp. 436-457. MR 0024004 (9:436i)
  • [6] R. E. Langer, The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point, Trans. Amer. Math. Soc. vol. 67 (1949) pp. 461-490. MR 0033420 (11:438b)
  • [7] -, On the asymptotic forms of the solutions of ordinary linear differential equations of the third order in a region containing a turning point, Trans. Amer. Math. Soc. vol. 80 (1955) pp. 93-123. MR 0073009 (17:365c)
  • [8] -, The solutions of the differential equation $ v''' + {\lambda ^2}zv' + 3\mu {\lambda ^2}v = 0$, Duke Math. J. vol. 22 (1955) pp. 525-542. MR 0073010 (17:365d)
  • [9] -, The solutions of a class of ordinary linear differential equations of the third order in a region containing a multiple turning point, Duke Math. J. vol. 23 (1956) pp. 93-110. MR 0079684 (18:127d)
  • [10] -, On the construction of related differential equations, Trans. Amer. Math. Soc. vol. 81 (1956) pp. 394-410. MR 0079159 (18:39b)

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DOI: https://doi.org/10.1090/S0002-9947-1957-0083637-0
Article copyright: © Copyright 1957 American Mathematical Society

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