Existence And Multiplicity Of Solutions For Critical Fractional Kirchhoff-Choquard Equations With Electromagnetic Fields

Variational method plays an important role in the application of nonlin-earity.This paper mainly studies the existence and multiplicity of solutions the non-trivial solutions for the critical fractional Kirchhoff-Choquard with elec-tromagnetic field on R~N.There are many difficulties in dealing with the loss of compactness due to the existence of both electromagnetic field and critical non-linear terms.In order to solve these difficulties,this paper uses the concentration-compactness principle to prove the compactness condition.The existence and multiplicity of solutions for the equation are proved by combining the moun-tain pass theorem and variational method.The structure of this paper is as follows:In chapter 1,this paper introduces the research background and the latest research progress at home and abroad.In chapter 2,the definition,theorem and lemma used in this paper are given.In chapter 3,firstly,the compactness condition is proved by the fraction-al concentration-compactness principle.Secondly,we proved that it satisfies the mountain pass theorem.Finally,the existence and multiplicity of solutions for the equation are proved.