Periodic solutions of the equation $\ddot x+g(x)=E \textrm {cos} t+\sigma h(t)\dot x$
Authors:
Luiz A. Ladeira and Plácido Z. Táboas
Journal:
Quart. Appl. Math. 45 (1987), 429-440
MSC:
Primary 58F14; Secondary 34C25
DOI:
https://doi.org/10.1090/qam/910451
MathSciNet review:
910451
Full-text PDF Free Access
References |
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Additional Information
- Jack K. Hale, Ordinary differential equations, 2nd ed., Robert E. Krieger Publishing Co., Inc., Huntington, N.Y., 1980. MR 587488
- W. S. Loud, Periodic solutions of nonlinear differential equations of Duffing type, Proc. U.S.-Japan Seminar on Differential and Functional Equations (Minneapolis, Minn., 1967) Benjamin, New York, 1967, pp. 199–224. MR 0223656
- W. S. Loud, Branching phenomena for periodic solutions of nonautonomous piecewise linear systems, Internat. J. Non-Linear Mech. 3 (1968), 273–293 (English, with French, German and Russian summaries). MR 234064, DOI https://doi.org/10.1016/0020-7462%2868%2990002-4
- W. S. Loud, Nonsymmetric periodic solutions of certain second order nonlinear differential equations, J. Differential Equations 5 (1969), 352–368. MR 235208, DOI https://doi.org/10.1016/0022-0396%2869%2990050-3
- L. F. Shampine and M. K. Gordon, Computer solution of ordinary differential equations, W. H. Freeman and Co., San Francisco, Calif., 1975. The initial value problem. MR 0478627
- A. Vanderbauwhede, Generic and nongeneric bifurcation for the von Kármán equations, J. Math. Anal. Appl. 66 (1978), no. 3, 550–573. MR 517746, DOI https://doi.org/10.1016/0022-247X%2878%2990253-6
J. K. Hale, Ordinary Differential Equations, 2nd ed., Kreiger Publ. Co., Huntington, N.Y. (1980)
W. S. Loud, Periodic solutions of nonlinear differential equations of Duffing type, Proc. US-Japan Seminar on Differential and Functional Equations, 199–224 (1967)
W. S. Loud, Branching phenomena for periodic solutions of non-autonomous piecewise linear systems, Internat. J. Non-Linear Mech. 3, 273–293 (1968)
W. S. Loud, Nonsymmetric periodic solutions of certain second order nonlinear differential equations, J. Differential Equations 5, 352–368 (1969)
L. F. Shampine and M. K. Gordon, Computer solutions of ordinary differential equations—the initial value problem, W. H. Freeman, New York, 1975
A. L. Vanderbauwhede, Generic and nongeneric bifurcation for the von Karman equations, J. Math. Anal. Appl. 66, 550–573 (1978)
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Article copyright:
© Copyright 1987
American Mathematical Society