Resonance in undamped second-order nonlinear equations with periodic forcing
Author:
George Seifert
Journal:
Quart. Appl. Math. 48 (1990), 527-530
MSC:
Primary 34C15; Secondary 70K30, 70K40
DOI:
https://doi.org/10.1090/qam/1074967
MathSciNet review:
MR1074967
Full-text PDF Free Access
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Additional Information
- G. R. Morris, A case of boundedness in Littlewood’s problem on oscillatory differential equations, Bull. Austral. Math. Soc. 14 (1976), no. 1, 71–93. MR 402198, DOI https://doi.org/10.1017/S0004972700024862
R. Dieckerhoff and R. Zehnder, Boundedness of solutions via twist theorem, Abteilung für Math. der Ruhr-Univ., Bochum 22 (1984)
- Tong Ren Ding, An answer to Littlewood’s problem on boundedness for super-linear Duffing’s equations, J. Differential Equations 73 (1988), no. 2, 269–287. MR 943943, DOI https://doi.org/10.1016/0022-0396%2888%2990108-8
- J. E. Littlewood, Unbounded solutions of an equation $\ddot y+g(y)=p(t)$, with $p(t)$ periodic and bounded, and $g(y)/y\rightarrow \infty $ as $y\rightarrow \pm \infty $, J. London Math. Soc. 41 (1966), 497–507. MR 197862, DOI https://doi.org/10.1112/jlms/s1-41.1.497
- José L. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17 (1950), 457–475. MR 40512
G. Morris, A case of boundedness in Littlewood’s problem on oscillatory differential equations, Bull. Austral. Math. Soc. 14, 71–93 (1976)
R. Dieckerhoff and R. Zehnder, Boundedness of solutions via twist theorem, Abteilung für Math. der Ruhr-Univ., Bochum 22 (1984)
T. Ding, An answer to Littlewood’s problem on boundedness for super-linear Duffing’s equations, J. Diff. Equations 73 (2), 269–287 (1988)
J. E. Littlewood, Unbounded solutions of an equation $\ddot y + g\left ( y \right ) = p\left ( t \right )$, with $p\left ( t \right )$ periodic and bounded and $g\left ( y \right )/y \to \infty$ as $y \to \pm \infty$, J. London Math. Soc. 41, 497–507 (1966)
J. Massera, The existence of periodic solutions of systems of differential equations, Duke Math. J. 17, 457–475 (1950)
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Article copyright:
© Copyright 1990
American Mathematical Society
