Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Some nonlocal results for weakly nonlinear dynamical systems

Authors: P. R. Sethna and T. J. Moran
Journal: Quart. Appl. Math. 26 (1968), 175-185
MSC: Primary 34.51
DOI: https://doi.org/10.1090/qam/240414
MathSciNet review: 240414
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References [Enhancements On Off] (What's this?)

  • [1] Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402
  • [2] Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
  • [3] N. M. Bogoliuboff and Yu. A. Mitropolskiy, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962
  • [4] Reference [3, Chap. 6]
  • [5] Joseph LaSalle and Solomon Lefschetz, Stability by Liapunov’s direct method, with applications, Mathematics in Science and Engineering, Vol. 4, Academic Press, New York-London, 1961. MR 0132876
  • [6] W. S. Loud and P. R. Sethna, Some explicit estimates for domains of attraction, J. Differential Equations 2 (1966), 158–172. MR 0190471, https://doi.org/10.1016/0022-0396(66)90040-4
  • [7] Reference [3], Chap. 4
  • [8] P. R. Sethna, Coupling in certain classes of weakly nonlinear vibrating systems, Internat. Sympos. Nonlinear Differential Equations and Nonlinear Mechanics, Academic Press, New York, 1963, pp. 58–70. MR 0152170
  • [9] Yu. A. Mitropolskiy, Problems of the asymptotic theory of nonstationary vibrations, Daniel Davey and Co., New York, 1965, Chaps. 4, 6
  • [10] P. R. Sethna, Domains of attraction of some quasi-periodic solvtions, to be published in Proceedings of the International Symposium on Differential Equations and Dynamical Systems, Mayaguez, Puerto Rico December 1965

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DOI: https://doi.org/10.1090/qam/240414
Article copyright: © Copyright 1968 American Mathematical Society

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