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| Boundedness of Solutions for Duffing Equationwith Low Regularity in Time |
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Citation： |
Xiaoping YUAN.Boundedness of Solutions for Duffing Equationwith Low Regularity in Time[J].Chinese Annals of Mathematics B,2017,38(5):1037~1046 |
| Page view： 2802
Net amount： 1555 |
Authors： |
Xiaoping YUAN; |
Foundation： |
Project supported by the National Natural Science
Foundation of China (No.11421061). |
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| Abstract： |
It is shown that all solutions are bounded for Duffing equation
$\ddot{x}+ x^{2n+1}+\sum\limits_{j=0}^{2n}P_{j}(t)x^{j}=0,$
provided that for each $n+1\le j\le 2n$, $P_j\in C^{\gamma}(\mathbb
T^1)$ with $\gamma>1-\frac1n$ and for each $j$ with $0\le j\le n$, $P_j\in
L(\mathbb T^1)$ where $\mathbb T^1=\mathbb R/\mathbb Z$. |
Keywords： |
Duffing equation, Boundedness of solutions, Lagrange stability, Moser twist theorem, Quasi-periodic solution |
Classification： |
34D20, 37J40, 70K43 |
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