Mountain Pass and Linking methods for elliptical semilinear variational inequalities: results of existence, stability and multiplicity

In this thesis we will deal with semilinear elliptic variational inequalities and we will discuss some results about existence, stability, and multiplicity obtained via variational methods. The main purpose of this thesis is to consider a completely new approach with respect to the papers already appeared in the literature. The fundamental tools used in this thesis to look for nontrivial solutions for the problem under consideration are a penalization method and some minimax theorems.