= Finite-time extinction in a sublinear Bernoulli equation
{title2=$T=(1-p)^{-1}\log[A/(A-y_0^{1-p})]$}
For $y'=y-Ay^p$, $A>0$ and $0<p<1$, put $u=y^{1-p}$ while $y>0$. Then $u'=(1-p)(u-A)$. If $0<y_0<A^{1/(1-p)}$, $u$ decreases to zero at the displayed finite time. The positive branch joins the zero solution with zero first derivative, giving a nonnegative forward solution. The equilibrium at zero is one-sided stable even though the vector field is not locally <Lipschitz continuous> there; the positive equilibrium is unstable.
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