Solution
= Solution
For $F(n)=\alpha n-\beta n^3$, the nonnegative equilibria are
$$
\boxed{n=0,
\qquad n=K:=\sqrt{\alpha/\beta}}.
$$
Since
$$
F'(0)=\alpha>0,
\qquad F'(K)=\alpha-3\beta K^2=-2\alpha<0,
$$
the zero equilibrium is unstable and $K$ is asymptotically stable.