The Existence Of Solutions For Schr(?)dinger-Poisson System And Nonlinear Schr(?)dinger-Bopp-Podolsky System

In this paper,we study the existence of ground state solutions and multiple solutions for fractional Schr(?)dinger-Poisson system and the existence and concentration of multiple solutions for nonlinear Schr(?)dinger-bopp-podolsky system by using variational method.The dissertation is divided into four chapters.The main contents are as follows:Chapter 1 We introduce some research backgrounds,recent research progress and then state the main results.Chapter 2 We state important theorems which will be used in the sequel.Chapter 3 We study the following fractional Schr(?)dinger-Poisson system(?)where p,q?(4,2s*),s ?(3/4,1),2s+2t>3,?>0 is a parameter.Under some assumptions made on the potentials K(x),a(x)and b(x),we established the existence of ground state solution and multiple solutions by the theory of Lusternik-Schnirelman category.Chapter 4 We study the following nonlinear Schr(?)dinger-Bopp-Podolsky system(?)With some suitable assumptions made on potential V(x)and f(u),we obtain the existence and concentration of the multiple solutions of the above system by means of Nehari manifold and the technique of constructing penalty function.