Multiplicity of solutions for a class of quasilinear equations with exponential critical growth

This paper deals with some results of existence and multiplicity of solutions for quasilinear problems involving the N-Laplacian operator, when the nonlinearity has exponential critical growth. To obtain our results we utilize Ekeland Variational Principle, Mountain Pass Theorem and inequalities of the type Trudinger-Moser. Bounded and unbounded domains are considered. (C) 2013 Elsevier Ltd. All rights reserved.