Existence results for a super-Liouville equation on compact surfaces

26 Sep 2019 · Jevnikar Aleks, Malchiodi Andrea, Wu Ruijun ·

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.