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

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  • 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 $g'\ge b>0$.
    Mathematics Subject Classification: Primary: 34C11, 34C15,34C25, 34C27, 34D05; Secondary: 34D23, 34D30.


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