We consider the SU(3) singular Toda system on a compact surface (Ï, g), where hiare smooth positive functions on Ï, ÏiâR+, pmâÏ and αim>-1.We give both existence and non-existence results under some conditions on the parameters Ïiand 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.
Battaglia, L., & Malchiodi, A. (2016). Existence and non-existence results for the SU(3) singular Toda system on compact surfaces. JOURNAL OF FUNCTIONAL ANALYSIS, 270(10), 3750-3807 [10.1016/j.jfa.2015.12.011].
Existence and non-existence results for the SU(3) singular Toda system on compact surfaces
Battaglia, Luca;Malchiodi, Andrea
2016
Abstract
We consider the SU(3) singular Toda system on a compact surface (Ï, g), where hiare smooth positive functions on Ï, ÏiâR+, pmâÏ and αim>-1.We give both existence and non-existence results under some conditions on the parameters Ïiand 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.| File | Dimensione | Formato | |
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