Inserted: 26 sep 2019
Last Updated: 25 may 2020
Journal: Trans. Amer. Math. Soc.
We are concerned with a super-Liouville equation on compact surfaces with genus larger than one, obtaining the first non-trivial existence result for this class of problems via min-max methods. In particular we make use of a Nehari manifold and, after showing the validity of the Palais-Smale condition, we exhibit either a mountain pass or linking geometry.
Keywords: super-Liouville equation, existence results, min-max methods