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
Full-text PDF Free Access
References |
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Additional Information
- Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955. MR 0069338
N. M. Bogoliuboff and Yu. A. Mitropolskiy, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962
Reference [3, Chap. 6]
- 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
- W. S. Loud and P. R. Sethna, Some explicit estimates for domains of attraction, J. Differential Equations 2 (1966), 158–172. MR 190471, DOI https://doi.org/10.1016/0022-0396%2866%2990040-4
Reference [3], Chap. 4
- 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
Yu. A. Mitropolskiy, Problems of the asymptotic theory of nonstationary vibrations, Daniel Davey and Co., New York, 1965, Chaps. 4, 6
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
J. K. Hale, Oscillations in nonlinear systems, McGraw-Hill, New York, 1963
E. A. Coddington and N. Levinson, Theory of ordinary differential equations, McGraw-Hill, New York, 1955, Chaps. 13, 14
N. M. Bogoliuboff and Yu. A. Mitropolskiy, Asymptotic methods in the theory of nonlinear oscillations, Gordon and Breach, New York, 1962
Reference [3, Chap. 6]
J. LaSalle and S. Lefschetz, Stability by Liapunov’s second method, Academic Press, New York, 1961, p. 59
W. S. Loud and P. R. Sethna, Some explicit estimates for domains of attraction, J. Differential Eqs. (2) 2, 158–172 (1966)
Reference [3], Chap. 4
P. R. Sethna, Coupling in certain classes of weakly nonlinear vibrating systems, in International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, J. P. LaSalle and S. Lefschetz, eds., Academic Press, New York, 1963
Yu. A. Mitropolskiy, Problems of the asymptotic theory of nonstationary vibrations, Daniel Davey and Co., New York, 1965, Chaps. 4, 6
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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Article copyright:
© Copyright 1968
American Mathematical Society
