The uniqueness of periodic solutions of Liénard equations in some domains including the origin (Q909087)

The authors establish sufficient conditions under which the Liénard equation \(\ddot x+f(x)\dot x+g(x)=0\) has the only periodic solution on a certain domain including the origin on which \textit{N. G. Lloyd} [Math. Proc. Camb. Phil. Soc. 102, 565-572 (1987; Zbl 0645.34021)] has proved the existence of periodic solutions. They require the Lloyd's conditions and supplementary ones having similar forms to be fulfilled. A sketch of proof is given.