The Study On The Existence Of Ground State Solutions For Fractional Schr(?)dinger Equations Of Choquard Type

As an important kind of elliptic equation,Schr(?)dinger equation of Choquard type is not only of great theoretical significance in the field of mathematics,but also has a wide range of applications in physics.In recent years,the existence,multiplicity and other properties of solutions for Choquard equation have been obtained by mathematical workers.In this paper,we study the existence of ground state solution for a class of fractional Schr(?)dinger system of Choquard type with non-periodic potentials.In this paper,we first prove that the functional has a Palais-Smale sequence on Nehari manifold by using Ekeland's variational principle.Then we use concentration compactness principle to tackle the lack of compactness of the sequence in(?)~N,and prove the existence of ground state solution,namely,under suitable assumptions of the potential functions,we respectively prove the existence and non-existence of ground state solution.The innovation of this paper is that we first study the existence of ground state solution for the above system.Moreover,compared with the existed Choquard system,the above system has potential functions.The study of this kind of problems can not only expand the basic theory of nonlinear analysis,but also promote the interdisciplinary application of mathematics in other disciplines.