Por Daniele Cassani (Università degli Studi dell'Insubria and RISM).

Abstract: We are concerned with existence and concentration of ground state solutions to a class of nonlocal Schrödinger equations. We consider the case in which the nonlinearity exhibits critical growth, namely in presence of the Hardy-Littlewood-Sobolev lower, as well as upper critical exponents. Assuming mild conditions on the nonlinearity and by using variational methods, we obtain existence and non-existence results. The limiting case of dimension two is also addressed. (Joint works in collaboration with: J. Zhang; J. van Schaftingen and J. Zhang; C. Tarsi and M. Yang).