= One-sided Lipschitz condition
{title2=$\operatorname{Re}\langle f(y)-f(z),y-z\rangle\leq\nu\|y-z\|^2$}
A one-sided Lipschitz condition controls the growth of distances between solutions of an <ordinary differential equation>. Differentiating the squared difference and applying the <Gronwall inequality> gives $\|y(t)-z(t)\|\leq e^{\nu t}\|y(0)-z(0)\|$. The case $\nu\leq0$ is a <dissipative vector field>. Ordinary <Lipschitz continuity> implies such a bound, but the converse fails: $f(y)=-y^3$ has one-sided constant zero on the real line without being globally <Lipschitz continuous>.
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