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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