A priori bounds for superlinear problems involving the N-Laplacian

In this paper we establish a priori bounds for positive solution of the N-Laplace equation in a bounded smooth domain in R^N, and with a nonlinearity having at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis-Merle to the N-Laplacian, in combination with the Trudinger-Moser inequality,the Moving Planes method and a Comparison Principle for the N-Laplacian.