Compactness, existence and multiplicity for the singular mean field problem with sign-changing potentials. Articles uri icon

authors

  • De Marchis, Francesca
  • LOPEZ SORIANO, RAFAEL
  • Ruiz, David

publication date

  • July 2018

start page

  • 237

end page

  • 267

volume

  • 115

International Standard Serial Number (ISSN)

  • 0021-7824

Electronic International Standard Serial Number (EISSN)

  • 1776-3371

abstract

  • In this paper we consider a mean field problem on a compact surface without boundary in presence of conical singularities. The corresponding equation, named after Liouville, appears in the Gaussian curvature prescription problem in Geometry, and also in the Electroweak Theory and in the abelian Chern–Simons–Higgs model in Physics. Our contribution focuses on the case of sign-changing potentials, and gives results on compactness, existence and multiplicity of solutions

keywords

  • prescribed gaussian curvature problem; conical singularities; variational methods; morse theory