On solutions of non-autonomous ordinary differential equations

This paper deals with the solutions of $m$th-order $m\geqslant 1$ differential equations of the form
$$ w^{(m)}=Q(r,w,\dots,w^{(m-1)}), $$
where $Q$ belongs to the Carathéodory class $K_{\mathrm{loc}}([a,\infty)\times\mathbb R^m)$, $a>0$.