Chetaev instability theorem

The Chetaev instability theorem for dynamical systems states that if there exists, for the system formula_1 with an equilibrium point at the origin, a continuously differentiable function V(x) such that
then the origin is an unstable equilibrium point of the system.
This theorem is somewhat less restrictive than the Lyapunov instability theorems, since a complete sphere (circle) around the origin for which V and formula_6 both are of the same sign does not have to be produced.
It is named after Nicolai Gurevich Chetaev.