Existence results for a super-Liouville equation on compact surfaces

Jevnikar, Aleks; Malchiodi, Andrea; Wu, Ruijun

doi:10.1090/tran/8209

Existence results for a super-Liouville equation on compact surfaces
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by Aleks Jevnikar, Andrea Malchiodi and Ruijun Wu PDF

Trans. Amer. Math. Soc. 373 (2020), 8837-8859 Request permission

Abstract:

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.

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