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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.

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    Nice question. But it appears $\dot r \ge r + r^5 - 2 r^3 = r (1 - r^2)^2 \ge 0$. So $r$ should go straight to infinity, shouldn't it? Then how come there is any periodic solution?2015-10-28

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