The discrete Lyapunov function for scalar differential delay equations (Q754055)

For the delay equation \(\dot x=f(x(t),x(t-1),t)\), one proves that a solution will tend to zero in a ``super-exponential'' manner if and only if the number of its zeros on the unit interval will tend to infinity. If f is periodic, the exponential decay rate is finite if the limit of number of zeros is finite and in this case the solution has an asymptotic exponential expansion.