Stability Of Ground States For The Schr(?)dinger-poisson Equation

In the last century,scholars have paid so much attention to Schr(?)dinger equation which is the basic equation of quantum mechanics.And Schr(?)dinger-Poisson equation is a local one particle approximation of the time dependent Hartree-Fock equations.In this thesis,we study the standing wave solution of Schr(?)dinger-Poission equation with subcritical power exponential.What's more,we establish the criterion of orbital stability.This thesis is divided into three chapters.The first chapter is an introduction,which describes the physical background of Schr(?)dinger-Poisson equation,related research results and the main conclusions of this thesis.In the second chapter,we introduce local well-posedness of Schr(?)dinger-Poisson equation and the variational characteristics of the ground state standing wave solution.The third chapter is to prove the main conclusions of this thesis.