Fractional problems with lack of compactness

Abstract

This research project focuses on the study of nonlinear elliptic problems driven by nonlocal fractional operators with lack of compactness. In particular, in this project we intend to work on the following directions.(1) In the first topic, with Prof. Patrizia Pucci (Università degli Studi di Perugia) and Prof. Binlin Zhang (HeilongjiangInstitute of Technology) we will study existence results for fractional systems involving critical terms.(2) In the second topic, joint with Dr. Vincenzo Ambrosio (Università degli Studi Urbino "Carlo Bo") we will study multiplicity results for fractional problems involving a critical Sobolev term and a Hardy potential.(3) Joint with Dr. Pawan Mishra (Universidade Federal da Paraíba), we will try to study fractional Kirchhoff type problems involving a Sobolev term and a singular one.(4) Finally, with Prof. Andrea Pinamonti (Università degli Studi di Trento) and Dr. Eugenio Vecchi (Università degli Studi di Bologna) we want to extend some classical existence and multiplicity results, proved for the Laplacian and the fractional Laplacian, to the complex case of the fractional magnetic Laplacian. (AU)