Existence of solutions to a higher dimensional mean-field equation on manifolds

Abstract

For $m\ge 1$ 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 $\lambda$.

15 Pages

References in corpus (1)

• Concentration-compactness phenomena in the higher order Liouville's equation