On the uniform attractivity of solutions of ordinary differential equations by two Lyapunov functions (Q1187015)

\textit{K. Murakami} and \textit{M. Yamamoto} [Proc. Japan Acad., Ser. A 64, 373-376 (1988; Zbl 0685.34061)] have given sufficient conditions for the global attractivity and equi-attractivity of the zero solution of the ordinary differential equation \(x'=f(t,x)\), \(f(t,0)=0\), \(x\in\mathbb{R}^ n\). The author shows that, after slightly strengthening one of them, the conditions in Murakami's and Yamamoto's theorem on global equi- attractivity imply even global uniform attractivity, and that global equi-attractivity can be assured under essentially weaker conditions.