Research On The Existence Of Solutions Of Several Quasilinear Schr(?)Dinger Equation In R

In this paper,we study the existence of nontrivial solutions or Normalized solutions for two quasilinear Schr(?)dinger equations in.which is divided into four chapters.Our paper is divided into four chapters as follows:In chapter 1,we briefly introduce the research background and research status for quasilinear Schr(?)dinger equations,and give the main notations and some preliminary lemmas.In chapter 2,we mainly study the following quasilinear Schrodinger equation in R(?).By variational method,we obtain the existence of multiple nontrivial solutions under some suitable assumptions on potential V(x)andf(x,u).In chapter 3,we study the existence and orbital stability of standing wave for quasilinear Schr(?)dinger equations with a general nonlinear term in,i.e.the following corresponding minimization problem with L~2-constraint:(?),Firstly,we discuss when the minimization sequence of E_? is compact,and show that there exists ?₀?0 such that when ?>?₀,there exists a global minimum and however there is no global minimizer when ?0.In addition,we discuss some conditions when?₀=0 or ?₀>0 and the existence results for E_?0 under some conditions.In chapter 4,we briefly summarize main content of our paper,and propose some problems which can be studied later.