On the asymptotic solutions of a class of ordinary differential equations of the fourth order. I. Existence of regular formal solutions

Authors:
C. C. Lin and A. L. Rabenstein

Journal:
Trans. Amer. Math. Soc. **94** (1960), 24-57

MSC:
Primary 34.00; Secondary 76.00

DOI:
https://doi.org/10.1090/S0002-9947-1960-0110865-8

MathSciNet review:
0110865

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References | Similar Articles | Additional Information

**[1]**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)****[2]**-,*On the asymptotic forms of the solutions of ordinary 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)****[3]**-,*The solutions of the differential equation*, Duke Math. J. vol. 22 (1955b) pp. 525-542.**[4]**-,*On the asymptotic solution of a class of ordinary differential equations of the fourth order, with special reference to an equation of hydrodynamics*, Trans. Amer. Math. Soc. vol. 84 (1957) pp. 144-191. MR**0083637 (18:738b)****[5]**-,*Formal solutions and a related equation for a class of fourth order differential equations of a hydrodynamic type*, MRC Technical Summary Report No. 22, to appear in Trans. Amer. Math. Soc. MR**0109923 (22:806)****[6]**C. C. Lin,*Theory of hydrodynamic stability*, Cambridge University Press, 1955. MR**0077331 (17:1022b)****[7]**-,*On uniformly valid asymptotic solutions of the Orr-Sommerfeld equation*, Proceedings of the Ninth International Congress of Applied Mechanics (Brussels) vol. I (1957) pp. 136-148.**[8]**-,*On the stability of the laminar boundary layer*, Symposium on Naval Hydro dynamics (National Research Council Publication 515), Washington, D. C., 1958, pp. 353-371.**[9]**-,*On the instability of laminar flow and its transition to turbulence*, Proceedings of the Symposium on Boundary Layer Theory (Freiburg), Springer, 1958, pp. 144-160.**[10]**A. L. Rabenstein,*Asymptotic solutions of the differential equation**for large values of the parameter*, Arch. Rational Mech. Anal. vol. 1 (1958) pp. 418-435. MR**0096855 (20:3337)****[11]**W. 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)****[12]**-,*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)****[13]**-, Discussion following paper by Lin, [8], ibid., pp. 363-366.

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DOI:
https://doi.org/10.1090/S0002-9947-1960-0110865-8

Article copyright:
© Copyright 1960
American Mathematical Society