I have the following theorem on the behaviour of ODEs with a vector field that is bigger than a linear polynomial. Let $f:\mathbb{R} \times \mathbb{R} \to \mathbb{R}$ be continuous and let $r,p,m,t_0 \in \mathbb{R}$ such that $p > 1, m > 0, r \ge 0$: If $\varphi:]\alpha,\omega[ \to \mat...