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Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 2009

Multiplicity results for the assigned Gauss curvature problem in R2

Résumé

To study the problem of the assigned Gauss curvature with conical singularities on Riemanian 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.
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Dates et versions

hal-00323700 , version 1 (22-09-2008)

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Jean Dolbeault, Maria J. Esteban, Gabriella Tarantello. Multiplicity results for the assigned Gauss curvature problem in R2. Nonlinear Analysis: Theory, Methods and Applications, 2009, 70 (8), pp.2870-2881. ⟨hal-00323700⟩
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