Multiplicity results for the assigned Gauss curvature problem in R2

Details Multiplicity results for the assigned Gauss curvature problem in R2 Multiplicity results for the assigned Gauss curvature problem in R2

2008-09-23

arxiv.org/abs/0809.3845v1

Mathematics

Analysis of PDEs

Nonlinear Analysis TMA (2009) to appear

Scientific paper

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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