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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References | Similar Articles | Additional Information

**[1]**Wolfgang Wasow,*A study of the solutions of the differential equation**for large values of*, 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*, 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