Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 931 - 973, Volume 28, Issue 3, November 2010      doi:10.3934/dcds.2010.28.931

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Gabriella Tarantello - Universitá degli Studi di Roma "Tor Vergata”, Dipartimento di Matematica, Via della Ricerca Scientifica, Roma, Italy (email)

Abstract: 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.

Keywords:  Mean field equations of Liouville type with singular sources, surfaces with conical singularies, electroweak vortices.
Mathematics Subject Classification:  53C21, 58J05, 35J60, 35J0, 35J05.

Received: March 2010;      Revised: April 2010;      Available Online: April 2010.