The Existence Of Solutions For Two Types Of Quasilinear Schr¨odinger Equations

In this paper,we firstly use the variational method to transform the existence of solutions for two types of quasilinear Schr?dinger equations into the existence of nontrivial critical point,which corresponds to the energy functionals of the equations.Then we apply the variable transformation to resolve the problem that energy functionals may not be defined in the usual Sobolev space H~1(R~N)corresponding to the original equations.At last,we prove the existence of solutions for two types of quasilinear Schr?dinger equations by using the Mountain pass lemma,Palais-Smale conditions,Cerami conditions and so on.This paper includes four chapters.The first chapter is an introduction.We mainly introduce the research background and research status of the article.In addition,we simply summarize the research content of the paper.In the second chapter,we give some definitions and lemmas.In the third chapter,we study the existence of ground state for the following quasilinear Schr?dinger equation under the circumstance that the nonlinear term h(u)satisfies superlinear condition by using the Mountain pass lemma,the Variational method,Lions lemma,Cerami conditions and so on.In the fourth chapter,we study the existence of ground states for the following quasilinear Schr?dinger equation under the circumstance that the nonlinear term f(x,u)satisfies the periodic condition by using the Mountain pass lemma,the Variational method,Palais-Smale conditions,Lions lemma and so on.