Asymptotic stability in the large of zero solution for Liénard equation (Q1309125)

Using results of \textit{G. Villari} and \textit{F. Zanolin} [Funkc. Ekvacioj, Ser. Int. 33, No. 1, 19-38 (1990; Zbl 0731.34049)] the author obtains new sufficient conditions for global asymptotic stability of the zero solution of the Liénard equation \(x''+ f(x)x'+ g(x)=0\) with \(g(0)=0\), \(xg(x)>0\) as \(x\neq 0\). These conditions are less restrictive than those given by \textit{H. Li} [Acta Math. Sin. 31, No. 2, 209-214 (1988; Zbl 0704.34059)], they cover certain situations where the function \(F(x)= \int^ x_ 0 f(s)ds\) does not satisfy \(xF(x)>0\) for all \(x\neq 0\).