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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Singular perturbations on the infinite interval
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by Frank Charles Hoppensteadt PDF
Trans. Amer. Math. Soc. 123 (1966), 521-535 Request permission
References
  • V. F. Butuzov, Asymptotic formulae for the solution of a system of differential equations on the semi-infinite interval $(0\leq t<\infty )$ with a small parameter multiplying the derivative, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1963 (1963), no. 4, 3–14 (Russian, with English summary). MR 0153932
  • Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
  • L. Flatto and N. Levinson, Periodic solutions of singularly perturbed systems, J. Rational Mech. Anal. 4 (1955), 943–950. MR 76126, DOI 10.1512/iumj.1955.4.54036
  • K. O. Friedrichs and W. R. Wasow, Singular perturbations of non-linear oscillations, Duke Math. J. 13 (1946), 367–381. MR 18308
  • 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 61241, DOI 10.1512/iumj.1954.3.53012
  • W. Hahn, On the general concept of stability and Liapunov’s direct method, Technical Rep. No. 485, U.S. Army Mathematics Research Center, Madison, Wisconsin, 1964.
  • J. L. Massera, On Liapounoff’s conditions of stability, Ann. of Math. (2) 50 (1949), 705–721. MR 35354, DOI 10.2307/1969558
  • A. N. Tihonov, Systems of differential equations containing small parameters in the derivatives, Mat. Sbornik N. S. 31(73) (1952), 575–586 (Russian). MR 0055515
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Additional Information
  • © Copyright 1966 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 123 (1966), 521-535
  • MSC: Primary 34.50
  • DOI: https://doi.org/10.1090/S0002-9947-1966-0194693-9
  • MathSciNet review: 0194693