Stability Of Standing Waves Of Two Classes Of Fractional Nonlinear Schr(?)dinger Equations

In this paper,we study the existence and stability of standing waves of two classes of fractional nonlinear Schrodinger equations.This thesis is divided into four sections according to contents.In Chapter 1,we introduce some background,methods and well-known results of classical and fractional nonlinear Schrodinger equations.We also give a comparison between these two equations.In Chapter 2,we present some preliminaries.In Chapter 3,by using the profile decomposition theory and variational methods,we prove the existence and stability of standing waves for the fractional Schrodinger equation with Choquard-type nonlinearity in the mass subcritical case.In Chapter 4.by using the profile decomposition theory and variational methods,we prove the existence and stability of standing,aves for the fractional Schrodinger equation with combined power-type and Choquard-type nonlinearities in the mass critical case.We extend the study of Bhattarai(J.Differential Equations 263:3197-3229,2017)to the mass critical case.