Calculus of Variations and Geometric Measure Theory

A. Jevnikar - A. Malchiodi - R. Wu

Existence results for a super-Liouville equation on compact surfaces

created by jevnikar on 26 Sep 2019
modified on 25 May 2020


Accepted Paper

Inserted: 26 sep 2019
Last Updated: 25 may 2020

Journal: Trans. Amer. Math. Soc.
Year: 2020


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