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

DOI10.1016/j.jfa.2015.12.011zbMath1338.35156arXiv1508.00929OpenAlexW1892232758MaRDI QIDQ265895

Luca Battaglia, Andrea Malchiodi

Publication date: 13 April 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.00929

zbMATH Keywords

blow-up analysisLiouville-type equationsmin-max solutionsnon-existence resultsPohožaev-type identitiesToda system

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Variational methods for elliptic systems (35J50) Elliptic equations on manifolds, general theory (58J05) Second-order elliptic systems (35J47) Blow-up in context of PDEs (35B44)

Related Items (17)

A variational approach to Liouville equations ⋮ A weak Trudinger-Moser inequality with a singular weight on a compact Riemannian surface ⋮ Degree counting formula for non-symmetric Toda systems of rank two ⋮ A double mean field equation related to a curvature prescription problem ⋮ The \(\operatorname{SU}(3)\) Toda system with multiple singular sources ⋮ Sharp upper bound of the number of solutions for the \(\mathrm{SU} (N + 1)\) Toda system on torus with non-critical parameters ⋮ Uniqueness of bubbling solutions with collapsing singularities ⋮ Existence of bubbling solutions without mass concentration ⋮ On number and evenness of solutions of the \(SU(3)\) Toda system on flat tori with non-critical parameters ⋮ Sharp estimates for solutions of mean field equations with collapsing singularity ⋮ Existence results for Liouville equations and systems ⋮ A unified approach of blow-up phenomena for two-dimensional singular Liouville systems ⋮ Analytical issues in the construction of self-dual Chern-Simons vortices ⋮ On singular Liouville equations and systems ⋮ MIN-MAX schemes for \(\mathrm{SU}(3)\) Toda systems ⋮ A general existence result for stationary solutions to the Keller-Segel system ⋮ Uniform bounds for solutions to elliptic problems on simply connected planar domains

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