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.
Titolo: | Existence and non-existence results for the SU(3) singular Toda system on compact surfaces | |
Autori: | ||
Data di pubblicazione: | 2016 | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jfa.2015.12.011 | |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
Parole Chiave: | Liouville-type equations; Min-max solutions; Non-existence results; Toda system; | |
Handle: | http://hdl.handle.net/11384/64420 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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BM-JFA-PP.pdf | BM-JFA-PP | Accepted version (post-print) | ![]() | Open Access Visualizza/Apri |
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