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), 2457
MSC:
Primary 34.00; Secondary 76.00
MathSciNet review:
0110865
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References 
Similar Articles 
Additional Information
 [1]
Rudolph
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.
67 (1949),
461–490. MR 0033420
(11,438b), http://dx.doi.org/10.1090/S00029947194900334202
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E. Langer, 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. 80
(1955), 93–123. MR 0073009
(17,365c), http://dx.doi.org/10.1090/S00029947195500730095
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, The solutions of the differential equation , Duke Math. J. vol. 22 (1955b) pp. 525542.
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Rudolph
E. Langer, On the asymptotic solutions of a class
of ordinary differential equations of the fourth order, with special
reference to an equation of hydrodynamics, Trans. Amer. Math. Soc. 84 (1957), 144–191. MR 0083637
(18,738b), http://dx.doi.org/10.1090/S00029947195700836370
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Rudolph
E. Langer, Formal solutions and a related
equation for a class of fourth order differential equations of a
hydrodynamic type, Trans. Amer. Math. Soc.
92 (1959),
371–410. MR 0109923
(22 #806), http://dx.doi.org/10.1090/S00029947195901099235
 [6]
C.
C. Lin, The theory of hydrodynamic stability, Cambridge, at
the University Press, 1955. MR 0077331
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, On uniformly valid asymptotic solutions of the OrrSommerfeld equation, Proceedings of the Ninth International Congress of Applied Mechanics (Brussels) vol. I (1957) pp. 136148.
 [8]
, On the stability of the laminar boundary layer, Symposium on Naval Hydro dynamics (National Research Council Publication 515), Washington, D. C., 1958, pp. 353371.
 [9]
, On the instability of laminar flow and its transition to turbulence, Proceedings of the Symposium on Boundary Layer Theory (Freiburg), Springer, 1958, pp. 144160.
 [10]
Albert
L. Rabenstein, Asymptotic solutions of
𝑢^{𝑖𝑣}+𝜆²(𝑧𝑢”+𝛼𝑢’+𝛽𝑢)=0
for large \vert𝜆\vert, Arch. Rational Mech. Anal.
1 (1958), 418–435. MR 0096855
(20 #3337)
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Wolfgang
Wasow, A study of the solutions of the differential equation
𝑦⁽⁴⁾+𝜆²(𝑥𝑦”+𝑦)=0
for large values of 𝜆, Ann. of Math. (2) 52
(1950), 350–361. MR 0037432
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Wolfgang
Wasow, Asymptotic solution of the differential equation of
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of Math. (2) 58 (1953), 222–252. MR 0061737
(15,874b)
 [13]
, Discussion following paper by Lin, [8], ibid., pp. 363366.
 [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. 461490. 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. 93123. MR 0073009 (17:365c)
 [3]
 , The solutions of the differential equation , Duke Math. J. vol. 22 (1955b) pp. 525542.
 [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. 144191. 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 OrrSommerfeld equation, Proceedings of the Ninth International Congress of Applied Mechanics (Brussels) vol. I (1957) pp. 136148.
 [8]
 , On the stability of the laminar boundary layer, Symposium on Naval Hydro dynamics (National Research Council Publication 515), Washington, D. C., 1958, pp. 353371.
 [9]
 , On the instability of laminar flow and its transition to turbulence, Proceedings of the Symposium on Boundary Layer Theory (Freiburg), Springer, 1958, pp. 144160.
 [10]
 A. L. Rabenstein, Asymptotic solutions of the differential equation for large values of the parameter , Arch. Rational Mech. Anal. vol. 1 (1958) pp. 418435. 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. 350361. 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. 222252. MR 0061737 (15:874b)
 [13]
 , Discussion following paper by Lin, [8], ibid., pp. 363366.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947196001108658
PII:
S 00029947(1960)01108658
Article copyright:
© Copyright 1960
American Mathematical Society
