Soliton Solutions To A Class Of Schr(?)dinger Equations

In this paper,we focus mainly on the existence of solutions for some Schrodingerequations:Firstly,the existence of nontrivial solutions for quasilinear Schrodinger quations; Secondly,the existence of nontrivial solutions for quasilinear Schrodinger equations withsubcritical or critical exponents.This paper is divided into three chapters. At Chapter Ⅰ,the historical background,research developments, main methods and achievements on nonlinear elliptic equationsare summarized. Then main conclusions of this paper are simply introduced.At Chapter Ⅱ, we study the existence of nontrivial solution for quasilinear Schrodingerequations. By using a change of variables, we get new equations for elliptic equations inSobolev space H1(RN).By studying variables G1(v) character, calculating the range of(?) and using Critical point theory as well as Mountain pass lemma,weget the existence of nontrivial solutions for Schrodinger equations.At Chapter Ⅲ, By using a change of variables, we get new equations. This equationsin this category is involving a convex-concave term. By using Critical point theory aswell as Mountain pass lemma,we get the existence of nontrivial solutions for Schrodingerequations.Next,we discuss the existence of nontrivial solutions for quasilinear Schrodingerequations with critical exponents.