On the asymptotic property of the ordinary differential equation (Q1826017)

The authors consider the asymptotic property of the zero solution of the equation (1) \(x'=f(t,x)\), \(f(t,0)=0\) where x and f belong to the n- dimensional real space \({\mathbb{R}}^ n\) with Euclidean norm, t is a real scalar and f is continuously differentiable on \(I\times {\mathbb{R}}^ n\), \(I=[0,\infty)\). By using a second Lyapunov's function they present conditions for the zero solution of (1) to be globally equi-attractive, and globally attractive.