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

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.

Citation: Yiqian Wang. Boundedness of solutions in a class of Duffing equations with a bounded restore force. Discrete and Continuous Dynamical Systems, 2006, 14 (4) : 783-800. doi: 10.3934/dcds.2006.14.783
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