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

DOI: 10.1016/j.na.2008.12.040

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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.

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Abstract

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.