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October  2006, 14(4): 783-800. doi: 10.3934/dcds.2006.14.783

Boundedness of solutions in a class of Duffing equations with a bounded restore force

Yiqian Wang 1,

1. 

Department of Mathematics, Nanjing Univerisity, Nanjing 210093, China

Received  October 2004 Revised  August 2005 Published  January 2006

In this paper, we consider the boundedness of all the solutions and the existence of quasi-periodic solutions for Duffing equations

$\frac{d^2x}{dt^2}+\arctan x=p(t),$

where $p(t+1)=p(t)$ is a smooth function.

Keywords: KAM theorem., Boundedness of solutions, bounded restore force.
Mathematics Subject Classification: Primary 34C99, 58F1.
Citation: Yiqian Wang. Boundedness of solutions in a class of Duffing equations with a bounded restore force. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 783-800. doi: 10.3934/dcds.2006.14.783
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