The notion of a well posed problem is related to the more common notion of stability as indicated by the following definition.

Definition: Consider the differential equation and without loss of generality, let the origin be an equilibrium point, i.e. . Then the origin is:

1. Stable, if a perturbation of the initial condition grows no larger than for subsequent times, i.e. if for
2. Asymptotically Stable, if it is stable and implies that
                          
grows no larger than for subsequent times, i.e. if for
3. Unstable if it is not stable.

Remark: This definition could also involve perturbations of , which are omitted for simplicity.

An autonomous system is one where does not explicitly depend on t, i.e.

If is an equilibrium point then, in this case, . Expanding the solution in a Taylor's series, we have

Since , we have