| Title | Existence and multiplicity result for the singular Toda system |
| Publication Type | Journal Article |
| Year of Publication | 2015 |
| Authors | Battaglia, L |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 424 |
| Pagination | 49 - 85 |
| ISSN | 0022-247X |
| Keywords | Existence result; Liouville-type equations; Multiplicity result; PDEs on compact surfaces; Toda system |
| Abstract | 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." |
| URL | http://www.sciencedirect.com/science/article/pii/S0022247X14010191 |
| DOI | 10.1016/j.jmaa.2014.10.081 |
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