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]**Earl A. Coddington and Norman Levinson,*Theory of ordinary differential equations*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR**0069338****[2]**L. Flatto and N. Levinson,*Periodic solutions of singularly perturbed systems*, J. Rational Mech. Anal.**4**(1955), 943–950. MR**0076126****[3]**K. O. Friedrichs and W. R. Wasow,*Singular perturbations of non-linear oscillations*, Duke Math. J.**13**(1946), 367–381. MR**0018308****[4]**I. S. Gradšteĭn,*On a class of nonlinear differential equations with small coefficients for certain derivatives*, Doklady Akad. Nauk SSSR (N.S.)**64**(1949), 441–443 (Russian). MR**0029033****[5]**J. J. Levin,*Singular perturbations of nonlinear systems of differential equations related to conditional stability*, Duke Math. J.**23**(1956), 609–620. MR**0080809****[6]**J. J. Levin and Norman Levinson,*Singular perturbations of non-linear systems of differential equations and an associated boundary layer equation*, J. Rational Mech. Anal.**3**(1954), 247–270. MR**0061241****[7]**A. N. Tihonov,*On systems of differential equations containing parameters*, Mat. Sbornik N.S.**27(69)**(1950), 147–156 (Russian). MR**0036902**

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

Article copyright:
© Copyright 1957
American Mathematical Society