2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33368Let $Ω$ be an annulus. We prove that the mean field equation $-Δψ=\frac{e\sp{-βψ}}{\int\sbΩe\sp{-βψ}} $ admits a solution with zero boundary for $β\in (-16π,-8π)$. This is a supercritical case for the Moser-Trudinger inequality.Filling a gap in the argument and adding 2 referrencesDifferential Geometrytext