Nonlinear Fractional Schrödinger Equations in R^N

The aim of this book is to collect a set of results concerning nonlinear Schrödinger equations in the whole space driven by fractional operators.The material presented here was mainly taken from some papers carried out by the author and some joint works with his collaborators in these last years.It concerns some existence, multiplicity, and regularity results and qualitative properties of solutions established by means of suitable variational and topological methods which take care of the nonlocal character of the involved fractional operator.We deal with fractional Schrödinger equations involving different types of potentials and nonlinearities satisfying certain growth assumptions.Moreover, fractional Kirchhoff problems, fractional Choquard equations, fractional Schrödinger-Poisson systems, and fractional Schrödinger equations with magnetic field are considered.The book is principally addressed to researchers interested in pure and applied mathematics, physics, mechanics, and engineering.It is also appropriate for graduate students in mathematical and applied sciences, who will find updated information and a systematic exposition of important parts of modern mathematics.In particular, the proofs are given in detail and some of them are presented in a more different and elegant way with respect to the original ones in order to make the exposition more accessible and attractive for the interested reader.