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. (c) 2008 Elsevier Ltd. All rights reserved.
Dolbeault, J., Esteban, M., Tarantello, G. (2009). Multiplicity results for the assigned Gauss curvature problem in R-2. NONLINEAR ANALYSIS, 70(8), 2870-2881 [10.1016/j.na.2008.12.040].
Multiplicity results for the assigned Gauss curvature problem in R-2
TARANTELLO, GABRIELLA
2009-01-01
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. (c) 2008 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
