Boundedness in a class of duffing equations with oscillating      potentials via the twist theorem

Huiping Jin

doi:10.3934/cpaa.2011.10.179

Article Contents

2011, Volume 10, Issue 1: 179-192. Doi: 10.3934/cpaa.2011.10.179

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Boundedness in a class of duffing equations with oscillating potentials via the twist theorem

Huiping Jin^1,

1.
Yiwu Industrial and Commercial College, Yiwu Zhejiang 322000

Received: October 31, 2009

Revised: July 31, 2010

Published: December 2010

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Abstract

In this paper, we prove the boundedness of all solutions and the existence of periodic and quasi-periodic solutions for the equation $\ddot{x}+x^{2n+1}+\sum_{j=0}^l x^j p_j (x,t)=0$, where $p_j (x,t)$ are smooth 1-periodic functions in both $x$ and $t$ with $n\geq 1, 0 \leq l \leq 2 n$.

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Mathematics Subject Classification: 37J40, 34C27.

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