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The study of semilinear problems with exponential nonlinearity has already been addressed by Liouville in the context of the problem of prescribing Gaussian curvature on a two-dimensional domain.

For this class of semilinear problems, the structure of the solutions has been studied in detail and has revealed quantization phenomena for blowing-up sequences of solutions.

In higher dimension, there are some analogous problems involving now the n-Laplacian, and we will see how those quantization results can be generalized.

This is a joint work with Pierpaolo Esposito (Università di Roma 3)