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Structure of the set of bounded solutions and existence of pseudo almost-periodic solutions of a Liénard equation. (English) Zbl 1212.34113
Summary: We study some of the properties of bounded, asymptotically almost-periodic or pseudo almost-periodic solutions of the Liénard equation \[ x''+f(x)x'+g(x)=p(t) \] where \(p:\mathbb R\rightarrow \mathbb R\) is a continuous, bounded, asymptotically almost-periodic or pseudo almost-periodic function, \(f\) and \(g\) \(:(a,b)\rightarrow \mathbb R\) are continuous and \(g\) is strictly decreasing. We describe the set of initial conditions of the bounded solutions on \((0,\infty )\) and we state some results on the existence of pseudo almost-periodic solution.

MSC:
34C11 Growth and boundedness of solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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