In this paper we consider the following Toda system of equations on a compact surface:-δu1=2Ï1(h1eu1â«Ïh1eu1dVg-1)-Ï2(h2eu2â«Ïh2eu2dVg-1)-δu1=-4Ïâj=1mα1,j(δpj-1),-δu2=2Ï2(h2eu2â«Ïh2eu2dVg-1)-Ï1(h1eu1â«Ïh1eu1dVg-1)-δu2=-4Ïâj=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, Ï1, Ï2 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=Ï1(heuâ«ÏheudVg-1)-Ï2(he-uâ«Ïhe-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].
Titolo: | A general existence result for the Toda system on compact surfaces | |
Autori: | ||
Data di pubblicazione: | 2015 | |
Rivista: | ||
Citazione: | 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]. | |
Handle: | http://hdl.handle.net/11590/330867 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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