Published in

Elsevier, Nonlinear Analysis: Theory, Methods and Applications, 8(70), p. 2870-2881

DOI: 10.1016/



Export citation

Search in Google Scholar

Multiplicity results for the assigned Gauss curvature problem in

Journal article published in 2009 by Jean Dolbeault ORCID, Maria J. Esteban, Gabriella Tarantello
This paper is available in a repository.
This paper is available in a repository.

Full text: Download

Green circle
Preprint: archiving allowed
Green circle
Postprint: archiving allowed
Red circle
Published version: archiving forbidden
Data provided by SHERPA/RoMEO


To study the problem of the assigned Gauss curvature with conical singularities on Riemannian manifolds, we consider the Liouville equation with a single Dirac measure on the two-dimensional sphere. By a stereographic projection, we reduce the problem to a Liouville equation on the Euclidean plane. We prove new multiplicity results for bounded radial solutions, which improve on earlier results of C.-S. Lin and his collaborators. Based on numerical computations, we also present various conjectures on the number of unbounded solutions. Using symmetries, some multiplicity results for non-radial solutions are also stated.