Abstract

In this paper we establish a priori bounds for positive solutions of the equation- ?N u = f (u), u ? H0 1 (O), where O is a bounded smooth domain in RN, and the nonlinearity f has at most exponential growth. The techniques used in the proofs are a generalization of the methods of Brezis and Merle to the N-Laplacian, in combination with the Trudinger-Moser inequality, the Moving Planes method and a Comparison Principle for the N-Laplacian. © 2008 Elsevier Inc. All rights reserved.