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.;Sire Y.
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.
2020
bubbling phenomena; existence of solutions; Mean field and Liouville equation; nonlocal equations
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1591023
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