Nonlinear Analysis

We study PDEs and systems of PDEs mainly nonlinear of elliptic type and in particular Schroedinger equations with local and nonlocal interactions both of variational and non-variational type. We also investigate relationship between optimal functional inequalities and quantization phenomena for related PDEs. We study qualitative properties of solutions, uniqueness of ground states and non-degeneracy. In dimension two interesting phenomena related to epsonential nonlinearities which we approach by topological variational methods. We also study fractional and higher order problems. The research group has tight collaborations with: Università di Pisa, Università di Milano, Università di Roma - La Sapienza, Chongqing Jiatong University - China, Zhejiang Normal University - China, Università di Lisbona, University of Brasilia, University of Rio de Janeiro, University of Bath - UK, Kyoto University - Japan, CIMS - NYU.