Existence results for mean field equations

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Let $Ω$ 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 referrences

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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/33368

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/dg-ga/9710023
 http://arxiv.org/abs/dg-ga/9710023

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arXiv