On a quasilinear mean field equation with exponential nonlinearity

2014/10/24 by Esposito, Pierpaolo, Morlando, Fabrizio · 1 citation
#35A15 #35B33 #35B44 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1410.6779

Abstract

The mean field equation involving the N-Laplace operator and an exponential nonlinearity is considered in dimension N≥2 on bounded domains with homogenoeus Dirichlet boundary condition. By a detailed asymptotic analysis we derive a quantization property in the non-compact case, yielding to the compactness of the solutions set in the so-called non-resonant regime. In such a regime, an existence result is then provided by a variational approach.

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