Proof:
Consider the nonlinear integro-differential equation
## \frac{dx}{dt}=-\lambda x(t)+\epsilon x(t)\int_{0}^{\infty}f(t-s)x(s)ds, \lvert \epsilon \rvert<<1, x(0)=A ##,
where ## \lambda ## is a positive constant and ## f(z) ## is a sufficiently well-behaved function.
Let ## \epsilon=0 ##...