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

In this paper,we mainly study the existence of bound state solutions for nonlinear Schr(?)dinger-Bopp-Podolsky system and fractional Schr(?)dinger-Poisson system by using the variational method.There are four chapters in this paper:In Chapter One,we summarize the background of the related problems and state the main results of the present paper.In Chapter Two,we study the existence of the positive bound state solutions for nonlinear Schr(?)dinger-Bopp-Podolsky system(?) where p E(3,5),potentials V(x),K(x)and Q(x)are positive functions and satisfy suitable assumptions.We prove the existence of the bound state solution by constraint minimization method,deformation lemma and constructing the surround structure.In Chapter Three,we study the existence of the positive bound state solutions for frac-tional Schr(?)dinger-Poisson system(?)where s,t?(0,1),2s+2t>3,p E(3,5).Under the suitable assumption of potential V(x),K(x)and Q(x),we prove the existence of positive bound state solution at high energy level by using the Nehari manifold method and deformation discussion.In Chapter Four,we summarize and prospect the research results of this paper.