01307nas a2200193 4500008004100000022001400041245009500055210006900150300001600219490000800235520066200243653002900905653002400934653002600958653001600984100002001000700002201020856007101042 2016 eng d a0022-123600aExistence and non-existence results for the SU(3) singular Toda system on compact surfaces0 aExistence and nonexistence results for the SU3 singular Toda sys a3750 - 38070 v2703 a
We consider the SU(3) singular Toda system on a compact surface (Σ,g)−Δu1=2ρ1(h1eu1∫Σh1eu1dVg−1)−ρ2(h2eu2∫Σh2eu2dVg−1)−4π∑m=1Mα1m(δpm−1)−Δu2=2ρ2(h2eu2∫Σh2eu2dVg−1)−ρ1(h1eu1∫Σh1eu1dVg−1)−4π∑m=1Mα2m(δpm−1), where hi are smooth positive functions on Σ, ρi∈R+, pm∈Σ and αim>−1. We give both existence and non-existence results under some conditions on the parameters ρi and αim. Existence results are obtained using variational methods, which involve a geometric inequality of new type; non-existence results are obtained using blow-up analysis and localized Pohožaev-type identities."
10aLiouville-type equations10aMin–max solutions10aNon-existence results10aToda system1 aBattaglia, Luca1 aMalchiodi, Andrea uhttp://www.sciencedirect.com/science/article/pii/S002212361500494201187nas a2200193 4500008004100000022001400041245006700055210006700122300001200189490000800201520057400209653002100783653002900804653002400833653002900857653001600886100002000902856007100922 2015 eng d a0022-247X00aExistence and multiplicity result for the singular Toda system0 aExistence and multiplicity result for the singular Toda system a49 - 850 v4243 aWe 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."
10aExistence result10aLiouville-type equations10aMultiplicity result10aPDEs on compact surfaces10aToda system1 aBattaglia, Luca uhttp://www.sciencedirect.com/science/article/pii/S0022247X1401019100409nas a2200109 4500008004100000245005900041210005900100260001000159653001600169100002000185856009400205 2015 en d00aVariational aspects of Liouville equations and systems0 aVariational aspects of Liouville equations and systems bSISSA10aToda system1 aJevnikar, Aleks uhttps://www.math.sissa.it/publication/variational-aspects-liouville-equations-and-systems