On the qualitative behaviour of solutions of Liénard equation (Q1088831)

Qualitative properties of the Liénard equation \(x''+f(x)x'+g(x)=0\) are obtained, where f,g:\({\mathbb{R}}\to {\mathbb{R}}\) satisfy appropriate conditions. In particular, the existence of a nontrivial periodic solution is established, and necessary and sufficient conditions are given for (1) all solutions to be oscillatory and (2) all solutions to be uniformly ultimately bounded.