TY - JOUR T1 - Existence and multiplicity result for the singular Toda system JF - Journal of Mathematical Analysis and Applications Y1 - 2015 A1 - Luca Battaglia KW - Existence result KW - Liouville-type equations KW - Multiplicity result KW - PDEs on compact surfaces KW - Toda system AB -

We consider the Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑j=1Jα1j(δpj−1),−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑j=1Jα2j(δpj−1), where hi are smooth positive functions, ρi are positive real parameters, pj are given points on Σ and αij are numbers greater than −1. We give existence and multiplicity results, using variational and Morse-theoretical methods. It is the first existence result when some of the αij's are allowed to be negative."

VL - 424 UR - http://www.sciencedirect.com/science/article/pii/S0022247X14010191 ER -