Asymptotic stability with respect to a first approximation in the broad sense (Q1374984)

The problem of asymptotic stability of an unperturbed motion for a system of ordinary differential equations is considered. The new approach is based on the first and second Lyapunov method and on a first linear and nonlinear approximation of the right-hand sides of the system of differential equations. Necessary and sufficient conditions are established for asymptotic stability of zero equilibrium points of the systems.