Some Existence Results and Properties of Solutions in Quasilinear Variational Inequalities with General Growths

This paper is about the existence and some properties of solutions of the boundary value problem: {−div(a(|∇u|)∇u)=f(x,u)inΩu=0on∂Ω, with the principal term a(|∇u|)∇u having general growth. In the non-coercive case, a sub-supersolution approach is applied to get existence and enclosure results. Other properties such as compactness of solution sets and existence of extremal solutions are also derived