We consider the fractional mean-field equation on the interval I = (-1, 1) (-Δ)1/2u = ρ eu/Ieudx, subject to Dirichlet boundary conditions, and prove that existence holds if and only if ρ < 2π. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.
The nonlocal mean-field equation on an interval / Delatorre, A.; Hyder, A.; Martinazzi, L.; Sire, Y.. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 22:5(2020). [10.1142/S0219199719500287]
The nonlocal mean-field equation on an interval
Delatorre A.;Martinazzi L.;
2020
Abstract
We consider the fractional mean-field equation on the interval I = (-1, 1) (-Δ)1/2u = ρ eu/Ieudx, subject to Dirichlet boundary conditions, and prove that existence holds if and only if ρ < 2π. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.File allegati a questo prodotto
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