*Consider a system
*

*$$
\begin{cases}
\dot{x}=f(x,y)\\
\dot{y}=g(x,y)
\end{cases}
$$*

*where $f$ and $g$ have continuous partial derivatives, and such that solutions exist for all $t$. Let $R$ denote a closed, bounded region of the $xy$-plane which contains no fixed points. Suppose that no solution may leave $R$. Then the system has a periodic solution in the region $R$.*