*Accepted Paper*

**Inserted:** 29 jan 2010

**Last Updated:** 17 jul 2018

**Journal:** Manuscripta Math.

**Year:** 2010

15 pages

**Abstract:**

For $m\geq 1$ we prove an existence result for the equation $$(-\Delta_{g)}^{m}
u+\lambda=\lambda\frac{e^{{2mu}}{\int}_{M} e^{{2mu}d\mu}_{g}$$} on a closed Riemannian
manifold $(M,g)$ of dimension $2m$ for certain values of $\lambda$.

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