Could anyone comment on the following ODE problem? Thank you.
Given a 2-d system in polar coordinates: $\dot{r}=r+r^{5}-r^{3}(1+\sin^{2}\theta)$ $\dot{\theta}=1$
Prove that there are at least two nonconstant periodic solutions to this system.
It's easy to prove that there is a noncostant periodic solution using Poincare-Bendixson theorem, but I don't know how to prove the existantce of two nonconstant periodic solutions.