Geodesic
On solutions of non-autonomous ordinary differential equations
Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 285-327.

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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 $K_{\mathrm{loc}}([a,\infty)\times\mathbb R^m)$, $a>0$. 
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A. A. Kon'kov. On solutions of non-autonomous ordinary differential equations. Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 285-327. http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a2/

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