The Orlicz-Sobolev spaces play a significant role in many fields of mathematics, such as approximation theory, partial differential equations, calculus of variations, nonlinear potential theory, theory of quasi-conformal mappings, differential geometry, geometric function theory, and probability theory. These spaces consists of functions that have weak derivatives and satisfy certain integrability conditions. The study of nonlinear elliptic equations involving quasilinear homogeneous type operators is based on the theory of Sobolev spaces Wm,p(Ω) and its goal is to find weak solutions. In the case of nonhomogeneous
differential operators, the natural setting for this approach are Orlicz-Sobolev spaces.