July  2010, 28(3): 931-973. doi: 10.3934/dcds.2010.28.931

Analytical, geometrical and topological aspects of a class of mean field equations on surfaces

1. 

Universitá degli Studi di Roma "Tor Vergata”, Dipartimento di Matematica, Via della Ricerca Scientifica, Roma, Italy

Received  March 2010 Revised  April 2010 Published  April 2010

We present some recent results on mean field equations of Liouville type over a closed surface, in presence of Dirac distributions supported at the so called "vortex points". We discuss possible existence and non-existence results as well as uniqueness and multiplicity issues according to the topological and geometrical properties of the surface.
Citation: Gabriella Tarantello. Analytical, geometrical and topological aspects of a class of mean field equations on surfaces. Discrete and Continuous Dynamical Systems, 2010, 28 (3) : 931-973. doi: 10.3934/dcds.2010.28.931
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