Boundedness and stability for the damped and forced single well Duffing equation

Cyrine Fitouri; Alain Haraux

doi:10.3934/dcds.2013.33.211

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2013, Volume 33, Issue 1: 211-223. Doi: 10.3934/dcds.2013.33.211

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Boundedness and stability for the damped and forced single well Duffing equation

Cyrine Fitouri^1, and
Alain Haraux^1,

1.
UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005, Paris

Received: July 31, 2011

Revised: December 31, 2011

Published: December 2012

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Abstract

By using differential inequalities we improve some estimates of W.S. LOUD for the ultimate bound and asymptotic stability of the solutions to the Duffing equation $ u''+ c{u'} + g(u)= f(t)$ where $c>0$, $f $ is measurable and essentially bounded, and $g$ is continuously differentiable with $g'\ge b>0$.

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Mathematics Subject Classification: Primary: 34C11, 34C15,34C25, 34C27, 34D05; Secondary: 34D23, 34D30.

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References

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