Periodic and quasi-periodic solutions of 1-d Q-curvature equation

We will discuss the existence of periodic or quasi-periodic solutions of the prescribed Q-curvature equation of circle with metric g as follows: $u^{(4)}+10 u^{(2)}+9u=\frac{9}{u^{5/3}}$. Some explicit $\pi$-periodic and $2\pi$-periodic solutions are well-known. We will discuss the existence of other type periodic solutions or quasi-periodic solutions of this equation via variation methods.