Noncoercive nonlinear elliptic equations in unbounded domains

This research thesis is mainly devoted to the study of noncoercive Dirich let problems with discontinuous coefficients in unbounded domains. The presence of the noncoercive operator does not allow us to use classical the orems to achieve existence results. Further complications arise as a conse quence of the unboundedness of the domain that yields to the lack of com pactness results. To overcome these difficulties, on one hand we approximate the solution of the problem by the solutions of suitable coercive nonlinear Dirichlet problems. On the other hand, we introduce suitable Sobolev spaces where opportune compactness results hold. [edited by Author]