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 NN-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.