The Existence And Multiplicity Of Sign-changing Solutions For Fractional Schr(?)dinger-Poisson System

In this paper,we study the following fractional Schrodinger-Poisson system(?)(1)where s ?(3/4,1),t ?(0,1)and 2s+2t>3,2s*=6/3-2s is the fractional critical exponent,the nonlocal operator(-?)?(?=s,t?(0,1))is the fractional Laplace operator.Under suitable assumptions on the potential V(x),K(x)and the nonlinear term f(x,u),we will prove the existence and multiplicity of sign-changing solutions for system(?)(1).The paper will be divided into five chapters as follows:Chapter 1.We introduce some research backgrounds,recent research progress and state the main result of this paper.Chapter 2.We state some elementary facts about fractional Sobolev space and some lemmas which will be used in the sequel.Chapter 3.When V(x)?1,f(x,u)=a(x)|u|p-2u+|u|2s*-2u and p ?(4,2s*),under the assumptions of K(x)and a(x),through using variational methods and Nehari manifold,we will establish the existence of ground state sign-changing solutions for system(1).Chapter 4.When K(x)? 1,under suitable assumptions on the potential V(x)and f(x,u),through using perturbation approach and invariant sets of descending flow method,we will prove the existence and multiplicity of sign-changing solutions for system(1).Chapter 5.We summarize the whole paper and give the research prospect.