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 h<inf>1</inf>, h<inf>2</inf> are smooth positive functions, Ï<inf>1</inf>, Ï<inf>2</inf> two positive parameters, p<inf>i</inf> points of the surface and α<inf>1,i</inf>, α<inf>2,j</inf> 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.
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. |
Handle: | http://hdl.handle.net/11590/330867 |
Appare nelle tipologie: | 1.1 Articolo in rivista |