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

Yiqian Wang

doi:10.3934/dcds.2006.14.783

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2006, Volume 14, Issue 4: 783-800. Doi: 10.3934/dcds.2006.14.783

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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

Received: September 30, 2004

Revised: July 31, 2005

Published: September 2006

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Abstract

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.

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Mathematics Subject Classification: Primary 34C99, 58F10.

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

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