Discrete conditions of Lyapunov stability
  We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right part of the differential equation instead of conditions on a Lyapunov function along trajectories of the equation. 
Eugene Polulyakh, Vladimir Sharko, Igor Vlasenko
math.CA math.DS