The Existence Of Solutions For A Class Of Sublinear Fractional Schr?dinger-Poisson Systems

Because the fractional Schr?dinger-Poisson system has important theoretical and practical significance,for the past few years,many scholars had paid great attention to it.In this master thesis,we discuss the following sublinear fractional Schr?dinger-Poisson systems with Sobolev critical exponent(?)where,?(0,1),0<<1,and(6,(1?~?(R~3).We suppose that()is a positive function and(6,(1 both change sign in R~3.This thesis is divided into three parts:In chapter one,we present the research background and current situation for Schr?dinger-Poisson systems.Then we also summarize the paper's structure and main research results.In chapter two,we introduce some of the notations and the main definitions involved for the present thesis.In chapter three,we study the existence of a solution for the sublinear fractional Schr?dinger-Poisson systems.In this thesis,the existence of infinite solutions of the system is obtained by applying Symmetric Mountain Pass theorem.