Given the following ODE in polar coordinates
\begin{array}{lcl} \frac{dr}{dt} = r\sin(\frac{1}{r}) \\ \frac{d\theta}{dt} = 1\end{array}
1) Show that the origin $(0,0)$ is Lyapunov stable
2) Prove that doesn't exist Lyapunov function
I could prove the first item, however I'm stuck in the second one. Any hint?