Study On Ground State Solutions And Sign-changing Solutions For Two Classes Of Schr(?)dinger-Poisson Problems

In this master thesis,we pay an attention on the existence of ground state solutions for the Schr(?)dinger-Poisson systems,and this master's thesis consists of four chapters:In chapter 1,we firstly introduce the background and the current research situation of two kinds of Schr(?)dinger-Poisson systems.Then briefly introduced the main results of this paper.In chapter 2,we give a brief introduction to some of the notations,definitions and relative knowledge used in this paper.In chapter 3,using the principle of variation,we investigate the existence of the ground state solution for the following Schr(?)dinger-Poisson systems.The nonlinear term in the system is a continuous function.Under appropriate assumptions on the nonlinear term,the ground state solution of the system is obtained by usying the variational principles such as mountain pass theorem and Lions lemma.In Chapter 4,the existence and asymptotic behavior of sign-changing solutions of minimum energy for a class of Schr(?)dinger-Poisson systems in bounded smooth regions are studied by using Ekeland variational principle,Sobolev inequality and implicit function theorem.The results obtained are the supplement and extension of the previous work.