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| Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation |
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Citation： |
Yaqun PENG,Xinli ZHANG,Daxiong PIAO.Boundedness of Solutions of a Quasi-periodic Sublinear Duffing Equation[J].Chinese Annals of Mathematics B,2021,42(1):85~104 |
| Page view： 713
Net amount： 680 |
Authors： |
Yaqun PENG; Xinli ZHANG;Daxiong PIAO |
Foundation： |
This work was supported by the National Natural Science Foundation of China (Nos.,11571327, 11971059). |
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| Abstract： |
The authors study the Lagrangian stability for the sublinear Duffing equations ddot{x}+e(t)|x|^{\alpha-1}x=p(t) with 0<\alpha<1,where e and p are real analytic quasi-periodic functions with frequency omega. It is proved that if the mean value of e is positive and the frequency omega satisfies Diophantine condition, then every solution of the equation is bounded. |
Keywords： |
Hamiltonian system, Sublinear Duffing equation, Boundedness, Quasiperiodic solution, Invariant curve |
Classification： |
34C11, 34D20, 37E40, 37J40 |
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