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| A Result on the Quasi-periodic Solutions of Forced Isochronous Oscillators at Resonance |
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Citation： |
Bin LIU,Yingchao TANG.A Result on the Quasi-periodic Solutions of Forced Isochronous Oscillators at Resonance[J].Chinese Annals of Mathematics B,2015,36(4):523~542 |
| Page view： 1167
Net amount： 959 |
Authors： |
Bin LIU; Yingchao TANG; |
Foundation： |
supported by the National Natural Science Foundation of China (No. 10325103) and the
Chinese Scholarship Council (No. 201206010092). |
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| Abstract： |
In this paper, the authors are concerned with the forced isochronous
oscillators with a repulsive singularity and a bounded nonlinearity
$$
x'' + V'(x) + g(x) = e(t,x,x'),
$$
where the assumptions on $V$, $g$ and $e$ are regular, described
precisely in the introduction. Using a variant of Moser's twist
theorem of invariant curves, the authors show the existence of
quasi-periodic solutions and boundedness of all solutions. This
extends the result of Liu to the case of the above system where $e$
depends on the velocity. |
Keywords： |
Isochronous oscillators, Repulsive singularity, Invariant curves, Time
reversibility, Quasi-periodic solutions, Lazer-Landesman conditions,
Boundedness of solutions |
Classification： |
70K43, 34C15 |
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