Аннотация:Using a particular example, we constructively prove that the convergence of allsolutions of a nonautonomous two-dimensional differential system to zero at infinity does not ingeneral imply even the partial Lyapunov stability of the zero solution, because it may happenthat each of the nonzero solutions at least once moves sufficiently far away from zero. In addition,the nonlinear system constructed in the present paper has zero first approximation along thezero solution.
