Existence And Multiplicity Of Solutions For Two Kinds Of Critical Choquard Term System

In recent years,fractional order elliptic system with Choquard term has been playing a more and more important role in many fields,and the research on the existence and other properties of the solution is of great significance and value.The paper mainly studies the existence,uniqueness and multiplicity of solution for two types of fractional elliptic system with Choquard term by using variational method.Firstly,this paper discuss the following fractional nonhomogeneous elliptic system with Choquard term:the uniqueness of the ground state solution for the homogeneous system and the multiplicity of the solutions for the nonhomogeneous system corresponding to problem(1)is proved by using variational method.Moreover,the global compactness result is obtained by using Palais-Smale sequence decomposition.Secondly,we discuss the following coupled fractional elliptic system with Choquard term nonlinearities:the existence of a positive solution for problem(2)at high energy level is proved by the Nehari manifold and the variational method.