Existence and comparison results for noncoercive and nonmonotone multivalued elliptic problems

We consider noncoercive quasilinear elliptic inclusions under multivalued flux boundary conditions involving multifunctions of Clarke’s generalized gradient. Our main goal is to provide existence and comparison results which are based on an appropriate generalization of the notions of subsolutions and supersolutions. Furthermore, compactness and extremality results of the solution set enclosed by an ordered pair of sub–supersolutions will be proved.