On a quasilinear mean field equation with exponential nonlinearity

الأصل · EN

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.