The asymptotic behavior of the stable initial manifolds of a system of nonlinear differential equations

Author:
J. J. Levin

Journal:
Trans. Amer. Math. Soc. **85** (1957), 357-368

MSC:
Primary 34.0X

DOI:
https://doi.org/10.1090/S0002-9947-1957-0088613-X

MathSciNet review:
0088613

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**[1]**E. A. Coddington and N. Levinson,*Theory of ordinary differential equations*, New York, 1955. MR**0069338 (16:1022b)****[2]**L. Flatto and N. Levinson,*Periodic solutions of singularly perturbed systems*, Journal of Rational Mechanics and Analysis vol. 4 (1955) pp. 943-950. MR**0076126 (17:849h)****[3]**K. O. Friedrichs and W. R. Wasow,*Singular perturbation of non-linear oscillations*, Duke Math. J. vol. 13 (1946) pp. 367-381. MR**0018308 (8:272d)****[4]**I. S. Gradstein,*On a class of non-linear differential equations with small coefficients for certain derivatives*, Doklady Akademii Nauk SSSR. (N.S.) vol. 64 (1949) pp. 441-443. MR**0029033 (10:536c)****[5]**J. J. Levin,*On singular perturbations of nonlinear systems of differential equations related to conditional stability*, Duke Math. J. vol. 24 (1956) pp. 609-620. MR**0080809 (18:305f)****[6]**J. J. Levin and N. Levinson,*Singular perturbations of non-linear systems of differential equations and an associated boundary layer equation*, Journal of Rational Mechanics and Analysis vol. 3 (1954) pp. 247-270. MR**0061241 (15:795f)****[7]**A. Tihonov,*On systems of differential equations containing parameters*, Rec. Math. (Mat. Sbornik) N.S. vol. 27 (69) (1950) pp. 147-156 MR**0036902 (12:181d)**

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DOI:
https://doi.org/10.1090/S0002-9947-1957-0088613-X

Article copyright:
© Copyright 1957
American Mathematical Society