In this paper we consider the following Toda system of equations on a compact surface:-δu1=2ρ1(h1eu1∫σh1eu1dVg-1)-ρ2(h2eu2∫σh2eu2dVg-1)-δu1=-4π∑j=1mα1,j(δpj-1),-δu2=2ρ2(h2eu2∫σh2eu2dVg-1)-ρ1(h1eu1∫σh1eu1dVg-1)-δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern-Simons theory. Here h1, h2 are smooth positive functions, ρ1, ρ2 two positive parameters, pi points of the surface and α1,i, α2,j non-negative numbers. We prove a general existence result using variational methods.The same analysis applies to the following mean field equation. -δu=ρ1(heu∫σheudVg-1)-ρ2(he-u∫σhe-udVg-1), which arises in fluid dynamics.

Battaglia, L., Jevnikar, A., Malchiodi, A., Ruiz, D. (2015). A general existence result for the Toda system on compact surfaces. ADVANCES IN MATHEMATICS, 285, 937-979 [10.1016/j.aim.2015.07.036].

A general existence result for the Toda system on compact surfaces

Battaglia, Luca;Malchiodi, Andrea;Ruiz, David
2015-01-01

Abstract

In this paper we consider the following Toda system of equations on a compact surface:-δu1=2ρ1(h1eu1∫σh1eu1dVg-1)-ρ2(h2eu2∫σh2eu2dVg-1)-δu1=-4π∑j=1mα1,j(δpj-1),-δu2=2ρ2(h2eu2∫σh2eu2dVg-1)-ρ1(h1eu1∫σh1eu1dVg-1)-δu2=-4π∑j=1mα2,j(δpj-1), which is motivated by the study of models in non-abelian Chern-Simons theory. Here h1, h2 are smooth positive functions, ρ1, ρ2 two positive parameters, pi points of the surface and α1,i, α2,j non-negative numbers. We prove a general existence result using variational methods.The same analysis applies to the following mean field equation. -δu=ρ1(heu∫σheudVg-1)-ρ2(he-u∫σhe-udVg-1), which arises in fluid dynamics.
2015
Battaglia, L., Jevnikar, A., Malchiodi, A., Ruiz, D. (2015). A general existence result for the Toda system on compact surfaces. ADVANCES IN MATHEMATICS, 285, 937-979 [10.1016/j.aim.2015.07.036].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/330867
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