# American Institute of Mathematical Sciences

January  2013, 33(1): 211-223. doi: 10.3934/dcds.2013.33.211

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

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

Received  August 2011 Revised  January 2012 Published  September 2012

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 $g'\ge b>0$.
Citation: Cyrine Fitouri, Alain Haraux. Boundedness and stability for the damped and forced single well Duffing equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (1) : 211-223. doi: 10.3934/dcds.2013.33.211
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##### References:
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