Existence and non-existence results for the SU (3) singular Toda system on compact surfaces

Battaglia, Luca;Malchiodi, Andrea
(2016) Journal of Functional Analysis — Vol. 270, n° 10, p. 3750-3807 (2016)

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  • Battaglia, LucaUCLouvain
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  • Malchiodi, AndreaUCLouvain
    Author
Abstract
We consider the SU(3) singular Toda system on a compact surface (σ, g), 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.
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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. https://doi.org/10.1016/j.jfa.2015.12.011 (Original work published 2016)