Bounded solutions of nonlinear second order ordinary differential equations (Q1576766)

The authors deal with the existence of bounded solutions on the whole real line to the forced Liénard equation \[ x''+f(x)x'+g(x)=e(t). \tag{1} \] Generalizations of recent results due to \textit{S. Ahmad} [Trans. Am. Math. Soc. 323, No.~2, 857-875 (1991; Zbl 0719.34062)] and \textit{R. Ortega} [Differ. Integral Equ. 8, No.~4, 729-734 (1995; Zbl 0817.34017)] are obtained. In case of a periodic forcing term, the established results allow to prove the existence of periodic solutions to (1).